Carpentry and Construction

231 calculators and reference tools for carpentry and construction. Every tool runs entirely in your browser. No account. No fee. No advertising. No tracking.

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Tools in this group

Stair Calculator - Risers, runs, and headroom from total rise.
Roof Pitch - Pitch as fraction, degrees, and percent.
Rafter Length - Rafter length from span, pitch, overhang.
Square Footage - Area for rectangle, triangle, trapezoid, circle.
Lumber Board Footage - Total board feet from thickness, width, length, count.
Concrete Volume - Cubic yards for slab, footing, column, footing-with-stem.
Rebar Spacing and Quantity - Linear feet of rebar from slab dimensions and spacing.
Lumber Spans - Maximum span from species, grade, size, load.
Nail and Screw Pull-Out - Typical pull-out resistance by fastener and species.
Beam Loading - Moment and deflection for simply supported beams.
Material Quantity - Quantity for common assemblies with waste factor.
Stair Stringer Length - Diagonal stringer length and 2x12 board feet from rise and run.
Joist Mid-Span Deflection - Mid-span deflection with L/360 and L/240 checks.
Footing Area for Soil Bearing - Required footing area and side dimension by soil class.
Tile Count and Grout Volume - Tile count with waste and grout cubic-inch estimate.
Paint Coverage - Gallons per coat by surface porosity and coats.
Excavation Volume - Cubic yards of soil for a sloped excavation.
Brick and CMU Count - Unit count from wall area, unit size, and mortar joint.
Wind Velocity Pressure - q = 0.00256 * V^2 with windward and leeward Cp.
Flat-Roof Snow Load - Pf = 0.7 * Ce * Ct * Is * Pg per public ASCE 7.
Anchor Bolt Embedment - Required embedment depth from public bond strength formula.
Drywall Sheet Count and Mud - Sheets, mud gallons, tape lf, and screws from wall and ceiling area.
Roofing Squares and Bundles - Squares, bundles per shingle product, underlayment rolls, drip edge.
Asphalt Tonnage - Tons of mix and truck loads at typical 20 tons per haul.
Aggregate / Gravel Cubic Yards - Cubic yards and tons from area, depth, and material density.
Mortar Mix and Yield - Bags of mortar mix from brick / CMU count and joint thickness.
Concrete Mix Design (Simplified) - Water-to-cement ratio interpolated from ACI 211-style curves; cement, coarse, fine aggregate per cubic yard.
Bolt Torque to Clamp Load - Short-form torque T = K * D * F with grade proof loads.
Sheet Metal Bend Allowance - Bend allowance and flat blank length from K-factor and angle.
Multi-Bend Flat Pattern (Developed Length) - The flat blank length for a sheet-metal part with several bends: flat = mold-line - n_bends x BD, the sum of the outside (mold-line) flange dimensions minus the bend deduction per bend (from bend-allowance). A U-channel of 2 + 4 + 2 = 8 in mold-line with 2 bends at 0.1355 in BD develops to 7.73 in; a hat section of 12 in mold-line over 4 bends develops to 11.46 in -- more bends pull more material out of the blank. A layout aid; confirm the first part against a test bend, since the real BD shifts with tooling, material, and grain.
Shop Speeds and Feeds - Spindle RPM and feed rate from SFM and chipload by tool / material.
Welding Rod and Wire Usage - Deposit weight, consumable weight, time, and shielding gas by process.
Demolition Debris Weight - Tons of debris and recommended dumpster size by structure type.
Formwork Pressure - Lateral form pressure (ACI 347 short form) capped at wet head.
Residential Framing Package - Stud + plate + joist + rafter rollup with board-feet totals from footprint, perimeter, wall height, joist span, rafter span, and pitch.
Excavation Slope and Bench-Step Plan - OSHA Appendix B slope ratios A 0.75:1 / B 1:1 / C 1.5:1 turned into spoil volume (yd^3), surface footprint, and bench-step layout. Competent person on-site governs the final plan.
Window / Door Header Sizing (IRC R602.7) - Smallest built-up dimension-lumber header (double / triple 2x6-2x12) from tributary load, span, snow, and species, with the AWC NDS bending / L-360 deflection check and IRC R602.7.5 jack-stud count.
Deck Beam and Post Sizing (IRC R507) - Deck beam ply and size, post size (4x4 / 6x6) from an NDS column check, footing size from soil bearing, and the IRC R507.9.1.3 ledger fastener spacing.
Braced-Wall-Panel Length (IRC R602.10) - Required braced-panel length (bracing percent x wall-line length), provided vs. required, and a pass/fail. Per IRC R602.10; the required percent is user-supplied from the adopted table.
Deck Ledger Fastener Spacing (IRC R507.9) - On-center spacing, fasteners for the ledger length, and a span/table check. Per IRC R507.9; the spacing is user-supplied from the adopted table for the fastener/span row.
Stair Stringer Layout (with code check) - Riser count, exact rise, total run, stringer hypotenuse, throat depth, and pass/fail against your AHJ's max rise / min tread.
Hip / Valley / Jack Rafter Schedule - Common-rafter and hip multipliers, jack-rafter shortening per OC, irregular-hip second pitch handling. Framing-square method.
Rebar Bend and Weight Schedule - Cut length with bend allowance and total weight by bar size from the bundled #3-#11 unit weights.
Plywood and OSB Sheathing Span Rating - Allowable spacing / live load / total load from APA span-rating tables; pass/fail against user-supplied design loads.
Helical Pile Torque-to-Capacity - Ultimate axial capacity from torque × Kt and allowable from factor of safety. Engineer of record governs.
Crane Lift Plan Quick-Math - Gross load, sling tension, percent of chart, and 75 / 90 percent flag. The crane manufacturer's load chart governs.
Bearing Length on a Wood Plate - Required bearing length and actual compression-perpendicular-to-grain stress for a point load on a wood plate, with a pass/fail against the allowable Fc-perp.
Wood Column Capacity (Slenderness) - Slenderness ratio, column stability factor Cp, allowable Fc-prime, and allowable axial capacity for a solid rectangular sawn-lumber column via the NDS Cp / Euler buckling basis.
Simple-Span Beam Reactions and Max Moment - Left/right reactions, max shear, and max bending moment for a simple-span beam under a uniform load plus an optional point load, by superposition.
Welding Heat Input - Heat input in kJ/in and kJ/mm from volts, amps, travel speed, and arc efficiency, with WPS pass/fail.
Metal Weight by Shape and Alloy - Weight per piece and total by shape, dimensions, length, and alloy density.
Layout Squaring (3-4-5) - Diagonal to pull and out-of-square diagnosis for a rectangular layout.
Horizontal Curve Layout - Tangent, length, external, middle ordinate, chord, and PC/PT stations for a circular curve.
Vertical Curve Elevations - Equal-tangent parabolic elevations and the high or low point of a vertical curve.
Earthwork Volume (End-Area) - Average-end-area and prismoidal earthwork volume in cubic feet and yards.
Slope-Stake Cut and Fill - Cut or fill depth and the catch-point offset for a planar design slope.
Superelevation / Min Curve Radius (AASHTO) - AASHTO point-mass e + f = V^2/(15 R): required superelevation for a radius, or the minimum radius at a maximum bank.
Crest Vertical Curve Length for SSD (AASHTO) - AASHTO minimum crest vertical-curve length L for a stopping sight distance, both S<=L and S>L branches, with the K rate.
Sag Vertical Curve Length for Headlight SSD (AASHTO) - The sag (valley) companion the crest tile hands off: a sag curve is limited at night by headlight reach, so its minimum length comes from the AASHTO headlight criterion L = A S^2/(400 + 3.5 S) for S<=L, L = 2 S - (400 + 3.5 S)/A for S>L, with K = L/A (400 and 3.5 embed the 2.0 ft headlight height and 1-degree beam). A 4% grade break needing 400 ft SSD wants a 350 ft sag curve (K 87.5). Headlight-SSD control only; comfort (A V^2/46.5) and drainage (K<=167) are separate. A design aid, not a substitute for a licensed civil engineer's design.
Horizontal Sightline Offset on a Curve (AASHTO) - AASHTO middle-ordinate clear-zone M = R(1 - cos(28.65 S/R)) an inside obstruction must clear for stopping sight distance.
Fillet Weld Strength and Size - Throat, ASD/LRFD shear capacity, utilization, and the AISC J2.4/J2.2b min/max fillet size for a steel fillet weld (AWS D1.1 / AISC 360).
Intermittent Fillet Weld Schedule (AISC J2 / AWS) - When a required continuous fillet is smaller than the practical minimum weld, sizes the intermittent (stitch) schedule that matches it: weld a fraction w_req/w of the length at the larger stitch size, pitch = increment / fraction, each increment at least the greater of 4 x the weld size or 1.5 in (AISC 360 J2.2b). A 3/16 in required weld done as 5/16 in stitches means welding 60% of the length; a 3 in increment gives a 5 in pitch (weld 3, skip 2) and clears the 1.5 in minimum. Maximum spacing and end returns are separate checks. A design aid, not a substitute for the engineer of record.
Groove Weld Strength - CJP / PJP groove-weld shear capacity on the effective throat (ASD / LRFD), with the CJP base-metal note and utilization (AWS D1.1 / AISC 360 §J2).
Press-Brake Air-Bend Tonnage - Air-bend press-brake tonnage from thickness, bend length, V-die opening, and tensile strength: tons/ft = 575 x (UTS/60) x T^2 / V (the published mild-steel 575 constant), with the 8 x T die and minimum-flange advisories (empirical air-bend rule).
Welder Duty Cycle - Allowable welder duty cycle at a target amperage from the rated amperage and duty cycle: DC2 = DC1 x (A1/A2)^2 (capped at 100%), minutes on per 10-minute window, and the maximum continuous amperage A1 x sqrt(DC1/100) (first-principles I-squared heating, NEMA EW-1).
Carbon Equivalent and Preheat Screen - IIW carbon equivalent CE = C + Mn/6 + (Cr + Mo + V)/5 + (Ni + Cu)/15 from the steel chemistry, with a plain-English weldability / preheat band (the formula adopted in AWS D1.1; a screen, not a welding procedure).
Shielding-Gas Cylinder Runtime and Cost - Gas used, runtime per cylinder, cylinders needed, and the prorated gas cost from a flow setting and arc-on time. Compressed-gas and hot-work hazards govern; follow the maker's instructions and your hot-work permit.
Oxy-Fuel Cutting Gas Consumption - Cut time, oxygen and fuel consumed, and runtime per cylinder for an oxy-fuel cut from the tip flows, cut length, and travel speed. The torch maker's tip chart sets the real flows; compressed-gas and flashback hazards govern.
Weld Preheat Energy and Fuel - Heat needed, fuel energy after efficiency, and propane in pounds and gallons to bring a steel mass to a preheat temperature. The preheat temperature comes from carbon-equivalent or the WPS; hot-work hazards govern.
All-In Welding Cost per Foot - Consumable per foot, filler cost, labor hours and cost, and the all-in cost per foot of weld -- where labor and the operating factor, not the filler, usually dominate. A real bid adds shop overhead, grinding, and power.
Weld Deposit Weight, Filler, and Pass Count - Weld cross-section, deposit weight, filler purchased after deposition efficiency, and the pass count for a fillet (by leg) or groove (by area) weld from first-principles joint geometry and steel density (0.2836 lb/in3). The WPS and the shop's measured deposition efficiency govern.
Wire Feed Speed to Deposition Rate - Melt-off rate from wire feed speed and electrode diameter, and the deposition rate after spatter loss, from first-principles wire-volume geometry and steel density. Pairs with weld-metal-volume for arc time. The WPS and process (spray vs short-circuit, gas) govern the real efficiency.
Weld Transverse Shrinkage and Pre-Set - Transverse shrinkage per weld and total pull from the Blodgett relation (0.2 x weld area / thickness), and the recommended pre-set to lay the parts apart so the assembly cools to size. A screen; restraint, sequence, and a mock-up govern, and longitudinal/angular distortion are out of scope.
Eccentric Fillet Weld Group (Elastic Method) - Line polar moment, direct shear, torsional components, the resultant unit force at the critical corner, and the required fillet leg for two vertical welds under in-plane eccentric load by the AISC elastic (vector) method. The conservative elastic method, a screen; the engineer of record governs.
Minimum Plate Bend Radius - Minimum inside bend radius and radius-to-thickness multiple to avoid cracking the outer fiber, from the published forming-limit relation R_min = T x (50 / %elongation - 1) and the mill-cert elongation. A screen; the mill cert, grain direction, and a test bend govern.
Weld Dilution Ratio - Weld dilution = melted base-metal area / total deposit area, the base-metal fraction of the deposit. A structural single-pass weld runs 30-40% (A_base 0.03, A_filler 0.05 -> 37.5%); a hardfacing overlay is kept low (16.7%) so the alloy stays near the filler. The WPS and filler data govern.
Weld Passes and Arc Time to Fill a Groove - Passes = ceil(groove area / area per pass), deposited weight = area x length x density, arc time = weight / deposition rate, total = arc / operator factor. A 12 in, 0.15 in^2 groove at 8 lb/h -> 5 passes, 0.51 lb, 3.8 min arc (9.5 min at 40%). The WPS and shop rates govern.
Weld Travel Speed for a Target Heat Input - Travel speed TS = (60 V I eta)/(1000 HI) to hold a target heat input; travel at or above it to stay at or under the limit. GMAW 24 V, 200 A, eta 0.8, 40 kJ/in -> 5.76 in/min; a 25 kJ/in ceiling forces 9.22 in/min. The qualified WPS governs.
Compound Miter (Crown Molding) - Saw settings to cut crown molding flat on the table: miter (table) = atan(tan(corner/2) x sin(spring)) and bevel (blade tilt) = asin(cos(spring) x cos(corner/2)) from the molding spring angle (38 or 45 degrees) and the wall corner angle (90 for a square corner) (first-principles trigonometry; reproduces the standard compound-miter chart).
Soil Swell / Shrinkage Volume Conversion - Convert bank (in-place) cubic yards to loose (truck) and compacted (placed) volume with the load factor and the borrow shortfall. The geotech report governs the percentages.
Haul-Cycle Production and Fleet Match - Truck cycle time, loads per hour, single-truck and matched-fleet production, and the number of trucks that keep the loader working.
Excavation Dewatering Pump Rate - Pump rate to draw an open excavation down in a target time and hold it against a steady inflow, with a safety-margined selection rate. Defers head to pump-tdh.
Trench Spoil Pile Setback and Surcharge - Required spoil-pile setback (the larger of the OSHA 2 ft minimum and the depth-based surcharge), the pile toe spread, and the total clear distance from the trench edge.
Trench Pipe Bedding and Backfill Take-Off - Bedding stone (cy and tons), pipe-zone embedment aggregate, and backfill volume for a pipe trench from the trench and pipe dimensions per ASTM D2321.
Coating Coverage from Volume-Solids and DFT - Theoretical and practical coverage, gallons, and the wet-film thickness from a coating's volume-solids and a target dry-film thickness (SSPC/AMPP PA 2; 1604 constant).
Abrasive Blast Air and Abrasive Consumption - Nozzle air-flow (cfm), compressor horsepower, abrasive consumption (lb/hr), and total abrasive for an area from the nozzle bore and blast pressure.
Fence Material Takeoff - Section, post, rail, and picket counts for a straight fence run from the run length, post spacing, rails per section, and picket width. Corner/end/gate posts are field-judgment extras.
Concrete per Post Hole - The concrete a batch of post holes needs: the cylinder volume of each hole less the post's displacement, totaled and divided into bags. For a fence, deck, sign, or mailbox.
Thin-Set Mortar Coverage - The bags of thin-set a tile job needs, sized off the trowel notch the way a setter buys it -- a 1/4 in notch covers about twice the area of a 1/2 in notch. tile-count gives the tile and grout.
Resilient / LVP Flooring Takeoff - Boxes of plank or tile to order at the waste allowance for the install pattern (straight / diagonal / herringbone), with the last-row balance that tells you whether to rip the first course.
Concrete Control Joint Spacing - Where to cut contraction (control) joints in a slab: the spacing in feet (about 2-3 times the slab thickness, capped), the saw-cut depth (a quarter of the slab), and the panel grid with an aspect-ratio check.
Rebar Lap-Splice Length - The tension lap-splice length as a multiple of the bar diameter (the jobsite 40-48 bar-diameter rule), with a 12 in floor and a feet-and-inches readout. The engineer of record and the drawings govern.
Paver Patio Takeoff - Pavers to order with a cut allowance from the patio area and paver face, plus the compacted base-aggregate and bedding-sand volumes underneath, in cubic yards.
Segmental Retaining Wall Takeoff - Blocks per course and number of courses (with the buried first course), total and cap blocks, and base-trench and drainage gravel for a segmental wall. Over 4 ft needs an engineered design with geogrid.
Attic Ventilation Net Free Area - The net free vent area an attic needs (the IRC 1/150 rule, or 1/300 balanced with a vapor retarder), the 50/50 intake/exhaust split, and the soffit-vent count and ridge-vent length.
Powered Attic Ventilator Sizing - The fan size and matching intake for a powered attic ventilator: fan CFM = attic floor area x ~0.7 CFM/ft^2 (about 10 air changes/hr), with a ~15% increase for a dark roof, and the required intake (soffit) net free area of about 1 ft^2 per 300 CFM so the fan pulls outdoor air rather than starving. A 1,500 ft^2 attic needs a 1,050 CFM fan and 3.5 ft^2 (504 in^2) of intake; a dark roof pushes the fan to 1,208 CFM. Balanced passive ridge-and-soffit ventilation is often preferred and some codes restrict powered fans. A sizing aid; the fan manufacturer's data and the local code govern.
Gutter and Downspout Sizing - The gutter size and number of downspouts a roof needs: the adjusted (design) roof area from the plan area, the roof pitch, and the local rainfall intensity, then the gutter and downspout count.
Steel Beam Lateral-Torsional Buckling (AISC 360 F2) - The moment the actual bracing allows - the check steel-beam-flexure defers: an unbraced compression flange buckles sideways below the plastic moment. AISC F2 grades the unbraced length against Lp = 1.76 ry sqrt(E/Fy) and the F2-6 Lr; between them Mn falls linearly, beyond Lr the elastic Fcr governs. A W18x50 braced every 10 ft drops from 421 to 360 kip-ft, and at 20 ft to 200 - less than half the braced number, the cliff that forces a brace or a heavier shape. Doubly-symmetric compact I-shapes, entered Cb. A design aid, not the engineer of record's stamped design.
Steel Block Shear Rupture (AISC 360 J4.3) - The tear-out failure that pulls a tab of steel out of a bolted end or coped web along a combined tension-and-shear path - the separate check steel-beam-shear names, and the one that frequently governs over the bolts. Rn = 0.6 Fu Anv + Ubs Fu Ant, capped by yielding on the gross shear plane; three 3/4 in bolts in a 1/2 in A36 plate give 111.8 kip nominal (ASD 55.9), and tightening the end distance drops it - why the detail sheet holds the edges. One row, standard holes. A design aid, not the engineer of record's stamped design.
Steel Tension Member: Yield and Rupture with Shear Lag (AISC 360 D2/D3) - The missing axial-tension leg beside the flexure, shear, and column tiles: a brace, hanger, or truss diagonal is the lower of gross yielding Fy Ag and net rupture Fu U An, where the shear-lag factor U = 1 - xbar/L punishes a member connected through only some of its elements. An L4x4x1/2 bolted through one leg draws U = 0.80 and flips the governing limit from yielding to rupture - the penalty a straight Fy Ag estimate misses; weld the full section and it flips back. Single hole line, no stagger. A design aid, not the engineer of record's stamped design.
RC Tied Column Axial Capacity (ACI 318-19 22.4) - The column the RC beam tiles never supplied: a concentrically loaded short tied column carries Po = 0.85 f'c (Ag - Ast) + fy Ast, capped at 0.80 phi Po (phi = 0.65) for the accidental eccentricity a concentric load never truly avoids. A 16 in square 4,000 psi column with eight #8 Grade 60 bars gives Po = 1,228 kip and a 639 kip design capacity, with the longitudinal ratio checked against the ACI 1-8% band. No P-M interaction or slenderness - short, tied, concentric only. A design aid, not the engineer of record's stamped design.
Two-Way Slab Punching Shear at a Column (ACI 318-19 22.6) - The limit state that sets flat-plate thickness and footing depth: the column punches a truncated cone through the slab on the critical perimeter d/2 from its face. The stress is the least of 4, (2 + 4/beta), and (2 + alpha_s d/bo) times lambda sqrt(f'c) (alpha_s 40/30/20 interior/edge/corner), and phi Vc = 0.75 vc bo d. An interior 20 in column on a d = 6 in slab holds 118.4 kip; grow the column to 36 in and the large-column term takes over - the case a drop panel fixes. No moment transfer or shear reinforcement. A design aid, not the engineer of record's stamped design.
Standard Hook Development Length (ACI 318-19 25.4.3) - Where a straight bar cannot fit - a beam bar anchoring into a column - the detailer hooks it, and the hook develops in ldh = (fy psi_e psi_r psi_o psi_c / (55 lambda sqrt(f'c))) db^1.5, never less than max(8 db, 6 in). A #8 Grade 60 bar in 4,000 psi concrete needs 14.9 in; a #5 only 7.4 - the db^1.5 scaling a hook = multiple-of-db rule of thumb gets wrong. Companion to the straight-bar rc-development-length. Standard 90/180 hooks; headed bars separate. A design aid, not the engineer of record's stamped detailing.
Shallow Foundation Elastic (Immediate) Settlement - The serviceability check soil-bearing-capacity calls separate: a footing can be far below its bearing strength yet settle too much. The theory-of-elasticity immediate settlement Se = q B (1 - nu^2) Is / Es (Is ~0.82 rigid square) gives a 6 ft footing at 3 ksf on medium sand 0.64 in - under the customary 1 in limit - but halve the modulus and the same footing fails at 1.29 in. Sizes the footing against movement, not strength; consolidation and embedment are separate. A design aid, not the geotechnical engineer's report.
Deep Pile Axial Capacity in Clay (Alpha Method) - The analytical pile capacity beside helical-pile's torque correlation: in clay the alpha method takes Qult = alpha cu (pi D L) skin friction plus 9 cu (pi D^2/4) end bearing. A 16 in pile 40 ft into cu = 1 ksf clay carries 105 kip ultimate (88% in skin friction) and 35 kip allowable at FS 3 - and doubling the length nearly doubles it while the tip term stays put, which is why a friction pile is lengthened, not fattened. Single pile, uniform clay, total-stress method. A design aid; the geotechnical engineer and a load test govern.
Infinite Slope Stability Factor of Safety - The screen a site engineer runs before benching a hillside cut: for a shallow slide parallel to a long uniform slope, FS = (c' + gamma H cos^2 beta tan phi') / (gamma H sin beta cos beta). A 25 degree cut in c' = 200 psf, phi' = 30 soil holds at FS 1.78; strip the cohesion and the elegant tan phi'/tan beta remains - depth-independent, why dry sand stands exactly at its angle of repose. Translational only, no seepage - a circular Bishop analysis and pore pressure are the geotech's work. A screening aid, not a stability analysis.
Infinite Slope Stability with Seepage - Why a slope that stood dry all summer slides in the spring: with steady seepage parallel to the slope and the water table at the surface, FS = (c' + (gamma_sat - 62.4) H cos^2 beta tan phi') / (gamma_sat H sin beta cos beta). The pore pressure cuts the friction term to the buoyant weight while the driving weight stays saturated, so a cohesionless factor of safety drops to (gamma_sat - 62.4)/gamma_sat -- about half. A phi = 32 sand at 18 degrees is a safe 1.92 dry but a failing 0.96 wet; the tile shows both so a subdrain's value is obvious. Translational, drained, no seismic. A screening aid, not a stability analysis.
Wood Bearing Perpendicular to Grain (NDS 3.10) - The crushing check a framer skips until the beam sinks into the plate: where a joist or beam lands across the grain, fc_perp = R/(b x lb) must clear Fc_perp x Cb, where the NDS 3.10.4 bearing-area factor Cb = (lb + 0.375)/lb rewards a short interior bearing. An 800 lb joist on 1.5 in of DF-L plate runs at DCR 0.46 and needs only 0.85 in; put a 6,000 lb beam reaction on the same footprint and it fails at 3.4x, demanding 6.4 in or a bearing plate. Fc_perp takes no load-duration factor. A design aid, not the engineer of record's stamped design.
Wood Tension Member Parallel to Grain (NDS 3.8) - The tie beside the strut: a truss bottom chord or collector checks ft = T/An against Ft x CD x CF, where the net area deducts the bolt holes a gross-area estimate misses. A 2x6 DF-L chord carrying 3,000 lb through one 3/4 in bolt loses 14% of its section at the hole and runs at DCR 0.56; snow-duration CD 1.15 and a clean section relax it to 0.42 - the two levers the code gives a tension member. Single hole line, no stagger; the bolt itself is the wood-bolt-connection tile. A design aid, not the engineer of record's stamped design.
Wood Beam-Column Interaction (NDS 3.9.2) - A stud carrying wind on a bearing wall is a beam and a column at once: NDS 3.9.2 combines them as (fc/Fc')^2 + fb/[Fb'(1 - fc/FcE)] <= 1.0, where FcE = 0.822 Emin'/(le/d)^2 and the 1 - fc/FcE denominator is the P-delta magnifier. A 4x4 stud at 3,000 lb + 3,000 in-lb passes at 0.55 with the bending term already amplified 1.6x; double the axial load and the amplifier nearly quadruples it to a 1.55 fail - the effect a designer must not drop. Enter Fc' with Cp and Fb' with CL from the companion tiles. A design aid, not the engineer of record's stamped design.
Steel Web Local Yielding and Crippling (AISC 360 J10) - Where a column bears on a beam or a beam lands on a plate, the web itself can fail before the member does: J10.2 web local yielding Rn = Fy tw (5k + lb) interior or (2.5k + lb) at an end, and J10.3 web crippling with its sqrt(E Fy tf/tw) term. Because their safety factors differ (1.50 vs 2.00), the governing limit can flip - a W18x50 on a 4 in interior bearing is crippling-governed at 102.1 kip ASD, but move the same bearing to the end and yielding takes over at 84.3 kip. The check that decides a bearing stiffener. A design aid, not the engineer of record's stamped design.
Slip-Critical Bolt Design Strength (AISC 360 J3.8) - Where slip cannot be tolerated - oversized holes, fatigue, load reversal - the joint is governed by friction, not shear: Rn = mu Du hf Tb ns with mu 0.30 (Class A) or 0.50 (Class B blast-cleaned), Du 1.13, and the Table J3.1 pretension. A 3/4 in A325 on a Class A surface resists 9.49 kip per bolt (6.33 ASD); go Class B in double shear and one bolt jumps 3.3x to 31.6 kip - surface prep and a second plane are the levers. The strength-level bolt-shear-bearing check must also pass. A design aid, not the engineer of record's stamped design.
Fillet Weld Size Limits and Effective Throat (AISC 360 J2.2b) - What size the code allows before the strength calc even applies: the Table J2.4 minimum leg from the THINNER part joined (so the weld cools slowly enough not to crack), the J2.2b maximum along an edge (full thickness under 1/4 in, thickness minus 1/16 at or over - so the edge is not melted away), the equal-leg throat 0.707 w, and the 4w minimum length. A 1/2 to 3/8 in joint takes a 3/16-to-5/16 window, and a chosen 1/4 in weld carries a 0.177 in throat. The numbers a WPS is written to; fillet-weld-strength assumes you already picked them. A fabrication aid; AWS D1.1 and the engineer govern.
Wind Components and Cladding Pressure (ASCE 7 Ch. 30) - The local envelope pressure wind-pressure cannot make: ASCE 7 Chapter 30 C&C design pressure p = qh [(GCp) - (GCpi)], where qh = 0.00256 Kz Kzt Kd Ke V^2 and GCpi = +/-0.18 (enclosed). A 115 mph Exposure C building draws qh 25.9 psf, and a roof corner (Zone 3, GCp = -1.8) sees -51.3 psf of suction - roughly double the field, the number a corner fastener and its spacing are designed for. GCp comes from the Ch. 30 zone figures (enter it). Local cladding pressure, not the whole-building MWFRS. A design aid, not the engineer of record's stamped design.
Snow Drift Surcharge at a Roof Step or Parapet (ASCE 7 Ch. 7) - The triangular surcharge that collapses lower roofs, which the flat-roof snow-load never adds: ASCE 7 Chapter 7 leeward drift height hd = 0.43 (lu)^(1/3) (pg + 10)^(1/4) - 1.5, density gamma = 0.13 pg + 14 (capped 30 pcf), peak pd = hd gamma over a 4 hd width. A 100 ft upwind roof at pg 30 psf piles 63 psf at the wall on top of the balanced load; a heavier 50 psf snow zone drives it to 83 psf. Leeward form, on top of snow-load's balanced number. A design aid, not the engineer of record's stamped design.
Rain-on-Snow Surcharge (ASCE 7-22 7.10) - The rain-on-snow surcharge added to the balanced flat-roof snow load where the ground snow Pg is 20 psf or less and the roof slope (deg) is less than W/50 (W the eave-to-ridge distance). ASCE 7-22 raised this to 5-8 psf (commonly 8) from the older flat 5, because a low-slope roof in wet-snow climates holds rain a steeper roof would shed. A Pf of 15 psf at Pg 18 low-slope becomes 23 psf; a deep-snow region (Pg 25) takes no surcharge, staying 15 psf. Balanced case only, both triggers required. A design aid, not a substitute for the engineer of record.
Sliding Snow Load on a Lower Roof (ASCE 7 7.9) - The surcharge from snow sliding off a slippery upper roof onto a lower roof: total = 0.4 x the upper roof's flat snow load Pf x its eave-to-ridge length W (lb/ft), distributed over the lesser of 15 ft or the lower-roof width. A 20 psf / 40 ft upper roof drops 320 lb/ft, which over 15 ft is a 21.3 psf surcharge; a narrow 10 ft catch roof concentrates the same total into 32 psf. Adds to the lower roof's own balanced load. A design aid, not a substitute for the engineer of record.
Minimum Roof Snow Load (ASCE 7 7.3.4) - The floor a low-slope roof's design snow load cannot fall below: Pm = Is x Pg where the ground snow Pg is 20 psf or less, or 20 x Is where Pg is over 20 (Is the snow importance factor). The design flat-roof snow is the greater of this minimum and the computed Pf, so the exposure/thermal/slope reductions cannot drop a low-slope roof below a single heavy snowfall. Pg 15 / Is 1.0 gives 15 psf; Pg 30 caps at 20 psf; Pg 25 with an essential-facility Is 1.1 gives 22 psf. Balanced case only. A design aid, not a substitute for the engineer of record.
ADA Ramp Slope, Runs, and Landings (IBC 1012 / ADA) - The full layout of an accessible ramp, not just the slope: run = rise x the slope ratio (max 1:12 / 8.33%), the number of runs = ceil(rise / 30 in) because a single run may rise only 30 in before a >=60 in landing, the landings that adds, and the total ramp length; handrails are required where the rise exceeds 6 in. A 24 in rise at 1:12 is one 24 ft run with handrails; a 40 in rise needs 2 runs and a 60 in landing for 45 ft of total ramp. A layout aid; the adopted code and ADA/ANSI A117.1 govern slope, width, and handrail details.
MWFRS Wall Pressure (ASCE 7 Ch. 27) - The lateral pressure the whole building resists, feeding the diaphragm and shear walls: ASCE 7 Chapter 27 MWFRS p = q G Cp - qi (GCpi), G = 0.85 rigid, Cp +0.8 windward / -0.5 leeward. A 25.9 psf building carries +22.3 psf on the windward wall (pushing in) and -15.7 psf on the leeward (suction), for a 28.6 psf net horizontal design pressure - the internal pressure cancels in the net, so the story force is insensitive to enclosure while the walls are not. Enter qz/qh from wind-pressure. Walls only. A design aid, not the engineer of record's stamped design.
Wind Force on Solid Freestanding Wall / Sign - Design wind force and Case B eccentric (torsion) moment on a solid freestanding wall, monument sign, or pylon: ASCE 7-22 Section 29.3, F = qh G Cf As with a net two-face Cf from Fig 29.3-1 (~1.2-2.0, not a building-wall +/- GCp). The 0.2B eccentricity, not the straight force, sizes the post and footing.
Unbalanced Snow Load on Gable Roof (ASCE 7 7.6.1) - The ASCE 7-22 7.6.1 unbalanced gable case: windward slope drops to 0.3 ps while the leeward carries ps plus a wind-blown ridge drift surcharge (hd gamma/sqrt(S)). Applies only in the ~1/2:12 to 7:12 slope band with W > 20 ft; sizes the leeward rafter and ridge the balanced case misses.
One-Way Slab / Beam Minimum Thickness for Deflection (ACI 318-19) - The depth that lets a designer skip a deflection calculation entirely: ACI 318-19 Table 7.3.1.1 / 9.3.1.1 gives l/20 simply supported, l/24 one end continuous, l/28 both continuous, l/10 cantilever, times (0.4 + fy/100,000) for non-Grade-60 steel and a lightweight factor. A simply supported 12 ft one-way slab needs 7.2 in; a both-ends-continuous Grade 40 slab only 4.1 in. The serviceability depth the strength tiles assume, for members not supporting damageable partitions. A design aid, not the engineer of record's stamped design.
Doubly-Reinforced Concrete Beam Flexural Capacity (ACI 318-19) - When a beam's depth is limited and the tension steel outruns a singly-reinforced section, the designer adds compression steel and the capacity gains a second couple A's fy (d - d'). ACI equilibrium gives a = (As - A's) fy / (0.85 f'c b) and Mn = the singly-reinforced couple plus the steel-to-steel couple. A 14x24 beam with As 8, A's 3 in^2 reaches 771 kip-ft (694 design) - above what the section could singly - and the compression steel both raises capacity and shrinks the stress block. Both layers assumed to yield (flagged if not). A design aid, not the engineer of record's stamped design.
Shear Friction Across an Interface (ACI 318-19 22.9) - The mechanism that carries shear across a cold joint, a corbel interface, or a wall-to-footing plane - not the beam-web diagonal-tension of rc-beam-shear: Vn = mu Avf fy, with mu 1.4 monolithic / 1.0 roughened / 0.6 unroughened / 0.7 to steel, capped by the concrete interface. 2.0 in^2 of Grade 60 dowels across a roughened joint carry 120 kip (90 design); add more dowels past the 153.6 kip cap and nothing changes because the concrete itself limits the transfer. Perpendicular (no net tension) case. A design aid, not the engineer of record's stamped design.
Concrete Modulus of Elasticity Ec (ACI 318-19 19.2.2) - Ec = wc^1.5 x 33 x sqrt(f'c) psi (ACI 19.2.2.1), the stiffness behind every deflection, drift, and short-column calculation; the normalweight shortcut is 57000 x sqrt(f'c). 4000 psi at 145 pcf -> 3,644,000 psi (3644 ksi); a 115 pcf lightweight deck is only ~70% as stiff. A design aid; the engineer of record's stamped design governs.
Concrete Modulus of Rupture fr (ACI 318-19 19.2.3) - fr = 7.5 x lambda x sqrt(f'c) psi (ACI 19.2.3.1), the tensile stress at which plain concrete first cracks, setting the cracking moment behind deflection and minimum-reinforcement checks. 4000 psi normalweight -> 474 psi (~0.119 f'c); all-lightweight (lambda 0.75) -> 356 psi. A design aid; the engineer of record's stamped design governs.
Shrinkage and Temperature Reinforcement (ACI 318-19 24.4) - Minimum shrinkage/temperature steel perpendicular to the main bars in a one-way slab: ratio 0.0018 (Grade 60) or 0.0020 (Grade 40/50), As,min = ratio x b x h, spacing <= min(5h, 18 in). A 6 in slab, Grade 60 -> 0.130 in^2/ft, 18 in max (about #4 at 18). A design aid; the engineer of record's stamped design governs.
T-Beam Effective Flange Width (ACI 318-19 6.3.2) - The slab width acting with a T-beam web: overhang = smallest of 8 hf, sw/2, ln/8 (interior; both sides) or 6 hf, sw/2, ln/12 (edge; one side). 12 in web, 4 in slab, ln 240, sw 48 -> be 60 in interior (sw/2 governs), 32 in edge (ln/12 governs). A design aid; the engineer of record governs.
Minimum Flexural Reinforcement As,min (ACI 318-19 9.6.1.2) - As,min = max(3 sqrt(f'c)/fy, 200/fy) x bw x d, so the beam does not fail suddenly at first cracking. 4000 psi, Grade 60, 12x20 -> 0.80 in^2 (200/fy floor governs); at 5000 psi the sqrt term governs, 0.85 in^2. A design aid; the engineer of record's stamped design governs.
Crack-Control Bar Spacing (ACI 318-19 24.3.2) - Max tension-bar spacing s = min(15(40000/fs) - 2.5 cc, 12(40000/fs)) for flexural crack control, fs = 2/3 fy typical. fs 40000, cover 2 in -> 10 in; more cover (3 in) tightens it to 7.5 in. A serviceability limit, not a strength check. A design aid; the engineer of record governs.
Concrete Bearing Strength (ACI 318-19 22.8) - The concrete-on-concrete bearing check that forgets the confinement bonus: Bn is not just 0.85 f'c x A1 -- when the supporting surface is wider than the loaded patch, the surrounding concrete confines it and the strength is multiplied by sqrt(A2/A1), capped at 2.0. A 12x12 in column (144 in^2) on a 36x36 in footing earns the full 2x -> phiBn = 636.5 kip (phi = 0.65); a pad flush to its support edge (A2 = A1) earns none -> 318.2 kip, exactly half. The tile returns the capped factor, nominal and design strengths, and the demand-capacity ratio. A design aid, not the engineer of record's stamped design.
Rebar Compression Development Length (ACI 318-19 25.4.9) - How deep compression dowels really go, which the tension development and hook tiles never answered: ldc = max(fy x psi_r / (50 lambda sqrt(f'c)) x db, 0.0003 fy psi_r db, 8 in). Compression development is SHORTER than tension because the bar end bears on concrete. A #8 Grade 60 dowel at 4,000 psi needs 19.0 in (the fy/sqrt(f'c) term governs); raise f'c to 8,000 psi and it stops falling at 18.0 in because the 0.0003 fy db floor takes over -- doubling the concrete strength did not shorten the dowel. Confining ties (psi_r = 0.75) drop it to 14.2 in. A design aid; the engineer of record's detailing governs.
Long-Term Deflection Multiplier (ACI 318-19 24.2.4) - Why bottom-only beams sag and doubly-reinforced ones hold: a concrete beam keeps deflecting for years from creep and shrinkage. ACI 24.2.4.1.1 multiplier lambda = xi / (1 + 50 rho'), where xi is 2.0 at 5+ years and rho' is the compression-steel ratio. A bottom-only beam (rho' = 0) with a 0.4 in immediate deflection gets the full lambda = 2.0 -> 0.80 in additional -> 1.20 in total, sagging triple its snapshot value; add compression bars so rho' = 0.01 and lambda drops to 1.33 -> 0.93 in total, 22% less. This long-term total is what the L/240 and L/480 limits are actually checked against. A design aid; the engineer of record governs.
Cast-In Anchor Tension Concrete Breakout (ACI 318-19 Ch. 17) - Concrete breakout capacity of a headed anchor in tension by the ACI 318-19 CCD method: Nb = kc lambda sqrt(f'c) hef^1.5 (kc 24 cast-in / 17 post-installed), edge-modified to Ncb and design phiNcb. The hef^1.5 cone and near-edge knockdown that anchor-embedment never checks; a near edge can cut capacity 25% before the steel yields.
Concrete Headed-Anchor Pullout (ACI 318-19 17.6.3) - The other tension failure mode concrete-anchor-breakout named as its companion: the head crushing through the concrete. Np = 8 x Abrg x f'c; Npn = psi_cP x Np (1.4 uncracked, 1.0 cracked); phiNpn = 0.70 x Npn. A 3/4-in headed bolt (0.654-in^2 head) in 4,000-psi cracked concrete pulls out at a factored 14.6 kip - and unlike breakout it does not depend on embedment, so deepening the anchor does not raise it. Headed anchors only (not adhesive or expansion). A design check, not a stamped anchor design.
Concrete Anchor Side-Face Blowout (ACI 318-19 17.6.4) - The third headed-anchor tension failure mode, the one deep anchors near an edge actually hit: Nsb = 160 x c_a1 x sqrt(Abrg) x lambda_a x sqrt(f'c), cut by (1 + c_a2/c_a1)/4 at a corner, phiNsb = 0.70 x Nsb. Governs when hef > 2.5 c_a1 - past that, deepening stops helping and the edge distance is the only knob. The v612 example anchor at a 3 in edge checks 17.2 kip design, and only 10.0 kip in a corner with a 4 in second edge. A design check, not a stamped anchor design.
Slender Column Moment Magnifier, Nonsway (ACI 318-19 6.6.4) - The ACI 318-19 6.6.4.5 nonsway P-delta moment magnifier delta_ns = Cm/(1 - Pu/(0.75 Pc)) and the magnified design moment Mc a slender braced reinforced-concrete column picks up. A column just over the slenderness limit gains a 1.3-1.7x amplifier the flexure check never applies; floored at M2,min.
Concrete Corbel / Bracket Design (ACI 318-19 16.5) - The primary tension steel of a concrete corbel or bracket by ACI 318-19 16.5: the mandatory 0.2 Vu horizontal tension, the greater of the flexure-plus-tension and shear-friction-plus-tension steel paths (which governs flips with the shear span), and the min-of-three shear cap. The corbel checks a bare shear-friction check misses.
Primary Consolidation Settlement (NC Clay) - The slow settlement that governs a foundation on clay, which soil-settlement-elastic names as separate: Sc = (Cc H/(1 + e0)) log10((sigma'0 + d_sigma)/sigma'0). A 10 ft NC clay (Cc 0.25, e0 0.90) under a 1,000 psf footing load settles 2.8 in - several times the immediate elastic dip, over years as water squeezes out. Because it grows with the LOG of the stress ratio, doubling the load increment only lifts it to 4.75 in - the first increment is the costly one. Single NC layer, no time rate. A design aid; the geotechnical engineer of record governs.
Eccentric Footing Bearing Pressure and Kern Check - The trapezoidal-or-triangular bearing pressure under a column with axial load plus moment, generalizing the wall check to any footing: while e = M/P stays in the middle-third kern (e <= B/6) the pressure is q = (P/BL)(1 +/- 6e/B); past it the heel lifts to a triangle over the front 3(B/2 - e). A 60 kip load on an 8 ft footing at e 1 ft runs 0.23 to 1.64 ksf full-bearing; push e to 2 ft and the toe spikes to 2.5 ksf with a third of the footing in no contact - the reason columns are kept concentric. Uniaxial, rigid footing. A design aid; the engineer of record governs.
Surcharge Lateral Pressure on a Wall from a Line Load (Boussinesq) - The bulge of lateral pressure a concentrated surface load (a footing, wheel line, or crane outrigger set back from a wall) puts on it - which the uniform Ka q surcharge never captures: the NAVFAC DM-7.2 modified-Boussinesq sigma_h = (0.203 qL/H) n/(0.16 + n^2)^2 for m <= 0.4, doubled for a rigid non-deflecting wall (m = x/H, n = z/H). A 1,000 lb/ft line 4 ft back from a 10 ft wall peaks near 97 psf at shallow depth; set it farther back and it pushes less and deeper. Line load, single depth. A design aid; the geotechnical engineer of record governs.
Steel Beam-Column Combined Axial and Flexure (AISC 360 H1.1) - The single number that decides a beam-column, which no single-action tile produces: AISC H1.1 combines axial and bending in a bilinear interaction - Pr/Pc + (8/9)(Mrx/Mcx + Mry/Mcy) for Pr/Pc >= 0.2, Pr/(2Pc) + (sum Mr/Mc) below. Pr 100 / Pc 400 with Mrx 80 / Mcx 200 passes at 0.61; drop the axial and the low-axial branch gives it a lighter half-weight, so a beam with only incidental axial is governed by its moment. Pc/Mc from the member tiles, in the same ASD or LRFD basis; second-order Mr assumed. A design aid, not the engineer of record's stamped design.
Column Effective Length Factor K (Alignment Chart) - The K that steel-column-capacity consumes but never computes: from the joint stiffness ratios G = sum(EI/L)_columns / sum(EI/L)_beams, the Dumonteil closed-form fits to the AISC alignment charts give sway K = sqrt((1.6 GA GB + 4(GA+GB) + 7.5)/(GA+GB+7.5)) and a braced form. GA 1, GB 2 gives K 1.47 sway but 0.82 braced - a factor of 3.2 in buckling capacity, why bracing a frame is the cheapest way to shorten a column. Enter G (or 10 pinned / 1 fixed); within ~2% of the nomograph, no tau_b. A design aid, not the engineer of record's stamped design.
Bolt Combined Tension and Shear (AISC 360 J3.7) - The tension a bracket, hanger, or moment end-plate bolt has left after its shear: AISC J3.7 reduces the nominal tensile stress F'nt = 1.3 Fnt - (Fnt/(phi Fnv)) frv, capped at Fnt. A 3/4 in A325 at 20 ksi required shear drops from 29.8 kip pure tension to 24.1 kip; a fully-sheared bolt floors at zero tension - the reduction a straight tension check misses. Bearing-type interaction (slip-critical is J3.9); the shear/bearing is the separate bolt-shear-bearing tile. A design aid, not the engineer of record's stamped design.
Relative Compaction from Field Density and Proctor Maximum - The pass/fail an earthwork inspector reads at every test point: RC = (field dry density / Proctor max) x 100, with the field dry density backed out of the nuclear-gauge wet density and moisture, gamma_d = gamma_wet/(1 + w). 128 pcf wet at 12% against a 120 pcf Proctor gives 114.3 pcf dry -> 95.2%, passing a 95% structural-fill spec; the same wet density at 16% moisture fails at 91.9% - the moisture reading is as important as the density, why over-wet fill is rejected. Enter the Proctor maximum (D698 / D1557). A QC aid; the geotechnical spec governs.
Soil Phase Relations (Void Ratio, Porosity, Saturation) - The three-phase makeup behind every settlement and bearing calc, made explicit: from the total unit weight, water content, and specific gravity Gs, the dry unit weight gamma_d = gamma/(1 + w), void ratio e = Gs gamma_w/gamma_d - 1, porosity n = e/(1 + e), and saturation S = w Gs/e. A 120 pcf soil at 15% and Gs 2.70 gives gamma_d 104.3 pcf, e 0.62, n 0.38, S 66% - the void ratio a consolidation needs, the saturation that says how much air is left to squeeze out. gamma_w = 62.4 pcf; enter Gs. An engineering aid; the soil test data govern.
Atterberg Plasticity Indices and A-Line Classification - The consistency numbers a geotech report leads with, and an earthwork spec screens fill against: the plasticity index PI = LL - PL, the liquidity index LI = (w - PL)/PI, and the USCS A-line PI = 0.73(LL - 20) that separates clay from silt. LL 45 / PL 22 gives PI 23 above the A-line 18.3 at LL < 50 -> CL lean clay, LI 0.35 (plastic/workable); a low-PI silt (LL 30, PI 5) plots below the A-line -> ML, the distinction that changes a fill's suitability. A-line chart classification, ASTM D4318. An engineering aid; the soil test data govern.
Nail Withdrawal Design Value (NDS 12.2.3) - The design number behind the framer's 'nails don't hold in withdrawal' instinct, which fastener-pullout only tabulates: NDS W = 1,380 G^(5/2) D lb/in, times the penetration. A 16d common nail (D 0.162) in DF-L (G 0.50) gives 39.5 lb/in, so a 1.5 in bite holds 59 lb; toenailed at wind duration the 0.67 Ctn nearly cancels the 1.6 CD bump - the reason toenailed uplift is weak and framing hardware replaces it. Side grain only (no end-grain withdrawal). A design aid, not the engineer of record's stamped design.
Lag Screw Withdrawal Design Value (NDS 12.2.1) - The lag's axial capacity from the NDS equation, not a table: W = 1,800 G^(3/2) D^(3/4) lb/in of thread penetration. A 1/2 in lag in DF-L over 4 in of thread holds 1,514 lb; step to a 5/8 in lag and it rises only 18% (the D^(3/4) law) - more or deeper lags beat one fat lag. Withdrawal (axial) value only, not the lateral yield-limit connection or the head bearing; end-grain installs take a 0.75 factor. A design aid, not the engineer of record's stamped design.
Wood Screw Withdrawal Design Value (NDS 12.2.2) - Why a screw that holds in fir strips in spruce: NDS W = 2,850 G^2 D lb/in scales with the SQUARE of specific gravity. A #10 screw (D 0.190) in DF-L (G 0.50) gives 135 lb/in; the same screw in softer SPF (G 0.42) drops 30% to 95.5 lb/in. Times the penetration for the withdrawal capacity. Axial withdrawal only, not the lateral connection or the head pull-through. A design aid, not the engineer of record's stamped design.
Cantilever Beam Moment, Shear, and Deflection - Max moment (P L + w L^2/2), max shear (P + w L), and tip deflection (P L^3/3EI + w L^4/8EI) of a cantilever from a tip point load, a uniform load, or both. Elastic small-deflection prismatic member. A design aid, not the engineer of record.
Cross-Section Properties (A, I, S, r) - Area, moment of inertia (I = b h^3/12 etc.), section modulus S = I/c, and radius of gyration r = sqrt(I/A) for a rectangle, solid round, pipe, or hollow tube. I scales with the cube of the depth, so orientation dominates. A design aid, not the engineer of record.
Combined Axial and Bending Stress (P/A +/- Mc/I) - Extreme-fiber stresses sigma = P/A +/- M c/I for a short member under axial force plus bending (or a moment from an eccentricity e). Reports whether the far face stays in compression (the kern threshold e <= r^2/c). Short member, no P-delta. A design aid, not the engineer of record.
Shaft Torsional Shear Stress and Angle of Twist - Polar moment J = pi(d^4-di^4)/32, max shear tau = T r/J, and twist theta = T L/(J G) for a solid or hollow circular shaft. A 1.5 in steel shaft at 1,000 lb-ft over 24 in -> 18,100 psi, 2.9 deg; a 2 in shaft cuts both far (the d^3/d^4 leverage). A design aid, not the engineer of record.
Restrained Thermal Stress and Force - A blocked member develops sigma = E alpha dT x restraint (independent of length) and force F = sigma A; the free expansion alpha L dT is what the restraint blocks. Steel +100 F fully restrained -> 18,850 psi; aluminum nets less. Heating = compression, cooling = tension. A design aid, not the engineer of record.
Thin-Wall Pressure Vessel Hoop and Longitudinal Stress - Hoop stress sigma_h = P D/(2t) and longitudinal sigma_l = P D/(4t) = half the hoop (why cylinders split lengthwise), valid for D/t >= 20. A 12 in tank, 0.25 in wall, 150 psi -> 3,600/1,800 psi. Not a substitute for the ASME BPVC or the engineer of record.
Design Spectral Response Accelerations SDS / SD1 (ASCE 7-22 11.4) - Site-adjust the mapped MCER accelerations (SMS = Fa Ss, SM1 = Fv S1) then take two-thirds for design (SDS = 2/3 SMS, SD1 = 2/3 SM1). Ss 1.0, S1 0.4, Site Class D (Fa 1.1, Fv 1.6) -> SDS 0.733g, SD1 0.427g, the exact inputs seismic-base-shear consumes. A design aid; the engineer of record governs.
Seismic Design Story Drift and Allowable Limit (ASCE 7-22 12.8.6 / 12.12) - Amplified drift delta_x = Cd delta_xe / Ie against the allowable delta_a = drift coefficient x story height (commonly 0.020 hsx). Cd 5.5, delta_xe 0.5 in, 144 in story -> 2.75 in vs 2.88 in allowable, OK at 0.955 utilization; a softer frame at 0.6 in fails. A design aid; the engineer of record governs.
Seismic P-Delta Stability Coefficient (ASCE 7-22 12.8.7) - theta = Px delta Ie / (Vx hsx Cd): below 0.10 neglect P-delta, up to theta_max = min(0.5/(beta Cd), 0.25) amplify by 1/(1-theta), above it the story is potentially unstable. Px 400 kip, Delta 2.75 in, Vx 80 kip -> theta 0.017, neglect; a soft story at theta 0.19 must be redesigned. A design aid; the engineer of record governs.
Guard and Handrail Code Check - Whether a guard and handrail meet the dimensional code: a guard is required where the walking surface is over 30 in above the floor below, with a 36 in (residential) or 42 in (commercial) minimum height, a 4 in sphere infill limit (4-3/8 in on the stair triangle), and a 34-38 in stair handrail. IRC R312 / R311.7.8 / IBC 1015; the assembly must also carry a 200 lb load and the AHJ governs.
Stair Geometry Code Check (IBC 1011 / IRC R311) - Whether a stair's riser, tread, and clear width meet the adopted code, the check every stair permit turns on: IBC (commercial) caps the riser at 7 in, floors the tread at 11 in, and needs 44 in of width; IRC (residential) allows a 7-3/4 in riser and a 10 in tread at 36 in. A 7-1/2 in riser is a legal residential stair and an illegal commercial one - the single most common tenant-improvement stair red-tag. Reports each dimension pass/fail against the selected code plus the 2R + T comfort read (24-25 in). Uniformity, nosing, landings, and winders are separate checks; the egress width from occupant load is the egress-capacity tile. A design aid, not a code-official determination; the AHJ governs.
CMU Grout Volume (Partial and Full Grout) - The grout volume for a reinforced CMU wall: grouted cores at the rebar spacing (cores = floor(len x 12 / spacing) + 1) plus a continuous bond-beam course, in ft^3 and cubic yards. Core and bond cross-sections come from the unit data; the spacing comes from the structural drawings and the engineer of record governs the reinforcement - a material takeoff, not a structural design.
Masonry Coursing and Course-Out Check - How many courses reach a height and whether that height lands on a module: course = unit + bed joint (CMU 8 in, three brick courses 8 in), courses = round(target / course), and a course-out flag when the wall top or opening is off-module and forces a cut course or fattened joints. Nominal dimensions; the product and the mason's joint govern - a layout aid, not a stamped elevation.
Wallcovering Roll Takeoff With Pattern Repeat - The rolls of wallcovering from the wall perimeter, height, and pattern repeat: full-height strips across the perimeter, one repeat wasted per strip to match the run, strips per roll, and rolls. A large repeat can nearly double the order for the same area. Roll size is the product's bolt size and openings are a manual credit - a material takeoff, not a hang plan.
Eave Ice-Barrier Membrane Courses and Rolls - The self-adhering ice-and-water membrane the eave actually needs: the up-slope coverage from the overhang and pitch (IRC R905.1.2 runs it 24 in inside the exterior wall line, measured on the slope), the courses when that exceeds one roll width, and the rolls. A deep overhang or a low pitch quietly pushes the coverage past a single 36 in course, so a one-roll-per-eave guess shorts the order. Required only where the AHJ has adopted it; valley and low-slope coverage is a separate add. A material takeoff, not a flashing plan.
Metal Roof Panels, Linear Feet, and Fasteners - Panels, linear feet, and through-fasteners (or clips) for one metal roof plane: the panel count from the product's net coverage width (not the sheet width), the total linear feet, the slope-area squares, and the fasteners from the wind-zone pattern. A 36 in exposed-fastener panel and a 16 in standing-seam panel covering the same plane differ by nearly a factor of two in panel count - which is why net coverage width, not square footage, sets a metal order. Per roof plane (double for a symmetric gable). A material takeoff, not a wind-uplift design.
Hip / Ridge Cap Bundles and Roofing Nails by the Pound - The two accessories the shingle field takeoff leaves open: the hip-and-ridge cap bundles from the ridge and hip linear feet, and the roofing nails by the pound. IRC R905.2.6 steps the field pattern from four nails to six in the high-wind / steep rows, which moves the order by half again, and a pre-formed hip/ridge product covers far less per bundle than field-cut 3-tab caps. Cap pattern and nail density come from the product wrapper and the adopted wind zone. A material takeoff, not a nailing schedule.
Roof Rain Load and Secondary-Drainage Flow (ASCE 7 Ch. 8) - The load that collapses flat roofs: standing water at the blocked-primary case. ASCE 7 Ch. 8 puts the rain load at 5.2 psf per inch of head - R = 5.2 x (static head to the secondary inlet + hydraulic head above it at design flow) - and the optional IPC design flow Q = 0.0104 x area x rainfall sizes the secondary drainage. Doubling the head to the overflow doubles the load, which makes the secondary inlet height a structural decision, not just a plumbing one. A flat roof must also pass the §8.4 ponding-instability check. A load and flow aid, not a stamped roof-drainage design.
ASCE 7 ASD Load Combinations: Governing Demand and Net Uplift - Combines dead, live, roof (snow/rain), and signed wind into the seven ASCE 7 §2.4.1 basic ASD combinations and returns the two cases the trades design to: the largest gravity demand (which sizes the beam, joist, or footing) and the most negative case (which, when 0.6D + 0.6W goes below zero, is the net uplift the roof-to-wall hold-down must resist). A member is never designed for one load at a time - the governing combination is, which is why the design starts here, not at the largest single load. A load-combination aid, not a member design.
Seismic Base Shear (ASCE 7 §12.8 Equivalent Lateral Force) - The earthquake demand on a regular building reduced to one equivalent static base shear: Cs = SDS / (R / Ie), capped at SD1 / (T x (R / Ie)) for T <= TL and floored at the code minimum, times the seismic weight. In much of the western US the seismic demand, not the wind, governs the lateral system - the shear walls, braced frames, hold-downs, and anchor bolts. A taller, more flexible building draws a smaller base shear because the period cap recognizes it rides the short-period spectral peak less. SDS / SD1 are from the USGS maps; R is from Table 12.2-1. A lateral-demand estimate, not a stamped seismic design.
Vertical Distribution of Seismic Forces (ASCE 7 §12.8.3) - The standard hand calc after the base shear: distribute V up the height as Fx = Cvx x V with Cvx = wx hx^k / Sum(wi hi^k), then take the story shears Vx by summing the forces at and above each level (§12.8.4). The exponent k (1 at T <= 0.5 s, 2 at T >= 2.5 s, interpolated between) is the whole story - softening a 3-story from T = 0.4 to 1.06 s shifts nearly 10 of 200 kips up to the roof. Levels enter one per line, bottom-up, as weight and height from the base; the base story carries the full V as the built-in check. Feeds the story shear the drift and P-delta tiles consume. A design aid; the engineer of record governs.
Seismic Overturning Moment (ASCE 7 §12.8.5) - The overturning the footing and the hold-downs resist, the next number after the vertical distribution: from the story forces Fx = Cvx x V, the base overturning moment M0 = Sum(Fi hi), the moment about each floor level (Sum of the forces above it times their height above it), and the 25% reduced foundation moment §12.13.4 permits at the soil interface. A 3-story with Fx = 37 / 74 / 89 kips at 12 / 24 / 36 ft carries 5,422 kip-ft at the base, 4,067 reduced. Levels enter one per line, bottom-up, as weight and height from the base; V and T come from seismic-base-shear. The resisting dead load, the foundation stability ratio, and the shear-wall hold-downs are separate checks. A design aid; the engineer of record governs.
Building Occupant Load from Area and Use (IBC Table 1004.5) - The one number the whole life-safety chain hangs on: the occupant load = sum over spaces of ceil(area / occupant-load factor). The factor is set by how the space is used, not its label - a 3,000 ft^2 office at 150 ft^2/occ is 20 people; the same floor as a standing bar at 5 ft^2/occ is 600. Bundled representative factors (business, assembly, mercantile, classroom, kitchen, industrial, storage, residential) are editable defaults; the factor and its net-vs-gross basis come from the AHJ-adopted code edition. A design aid, not a code-official determination.
Egress Exit Count and Required Width (IBC 1005.3 / 1006.2) - Turns the occupant load into the two egress demands: the number of separate exits (1 up to 49, 2 to 500, 3 to 1,000, 4 beyond) and the clear width per exit (occupant load x a capacity factor of 0.15 in/occ level or 0.2 in/occ stair when sprinklered, 0.2 / 0.3 without), divided among the exits and floored at the 32 in door-leaf minimum. For a modest load the exit count and the leaf minimum control, not the raw width. A design aid, not a code-official determination.
Minimum Plumbing Fixtures by Occupancy (IBC Table 2902.1) - The minimum water closets, lavatories, drinking fountains, and service sink a building must provide from its occupant load and occupancy class: fixtures = ceil(occupants-per-sex / ratio), each rounded up, load split evenly between the sexes. A 100-occupant office needs four water closets (the 1:25 first-tier ratio and the round-up push it past the naive per-50 read), where a 160-occupant restaurant on the 1:75 ratio needs far fewer. The occupancy class, not the head count alone, sets the fixtures. A design aid, not a code-official determination.
Formwork Shore Post Load and Spacing (ACI 347) - The vertical load path of an elevated pour: design pressure = max(slab_in/12 x unit weight + form load + construction live load, 100 psf floor), and the load on any one shore is that pressure times its tributary area. An 8 in slab on a 4 ft grid carries over 2,500 lb per post. Motorized buggies raise the live load to 75 psf and the floor to 125 psf. The rated capacity is the manufacturer's allowable for the extended height and bracing; reshoring and the slab below are separate analyses. A design aid, not a stamped shoring plan.
Concrete Surface Evaporation Rate and Plastic-Shrinkage Risk (ACI 305) - The finisher's go / no-go on plastic-shrinkage precautions, read off the day's weather: the ACI 305 / Menzel evaporation rate from the concrete and air temperatures, the humidity, and the wind. Above about 0.2 lb/ft^2/hr the surface cracks before it sets unless you fog, screen, retard, or cover. A 90 F, 40% RH, 15 mph pour evaporates several times faster than a calm humid one; the concrete temperature, not the air, drives it. A field screen, not a curing specification (curing follows ACI 308).
Concrete Age-Strength Gain for Form Stripping (ACI 209) - How much of its specified 28-day strength a slab has reached at a given age, the ACI 209R fraction t / (a + b t) times f'c - about 46% at 3 days, 70% at 7, 88% at 14 for Type I moist-cured - plus the inverse solve for the age to hit a target percent (commonly 75% to pull shores). The schedule decision behind every form-strip and shore-removal. An estimate of the mean trend, not a substitute for field-cured cylinder breaks; the engineer of record and the spec govern the actual strip strength.
Concrete Maturity and Equivalent Age (ASTM C1074) - The temperature-honest cure schedule: the Nurse-Saul time-temperature factor (Ta - T0) x hours in deg C-hr, the Arrhenius equivalent age at a 68 F reference, and the hours remaining to the mix's lab-calibrated TTF target. A 50 F week accrues 1,680 C-hr and reads as only 3.8 equivalent days - the cold slab is not '7 days old' - while three days at 90 F carry nearly six days of equivalent age. Datum 0 C and Q = 5000 K for Type I without admixtures, both editable. The strength a TTF represents comes only from the C1074 lab calibration of the actual mix; supplements, not replaces, acceptance cylinders.
Rebar Weight Takeoff - ASTM A615 nominal bar weight per foot x total linear feet, to tons and cost. A #5 bar (1.043 lb/ft) x 500 ft -> 522 lb (0.26 ton); a #8 (2.670) at the same length weighs 1,335 lb (0.67 ton), more than double for the #5-to-#8 jump. Rebar is bought by weight. Add lap and waste before the takeoff. The shop drawings and mill weights govern.
Ready-Mix Concrete Order (Trucks, Waste, Short Load) - Ordered = in-place volume x (1 + waste%), trucks = ceil(ordered/capacity), short-load fee below the plant minimum. 42 yd^3 at 8% waste, 10 yd^3 trucks -> 45.4 yd^3, 5 trucks, 5.4 yd^3 last load, no fee; a small 6 yd^3 pour trips the sub-10 yd^3 short-load fee. Ordering a little long beats a second delivery. The supplier's terms govern.
Insulation Batt Coverage and Count - Batts and bags from the net cavity area / coverage per batt and per bag, at a waste allowance. 500 ft^2, R-13 batt (10.67 ft^2), 88 ft^2/bag -> 47 batts, 6 bags; a deeper R-21 bag covering 67 ft^2 raises it to 8 bags for the same wall. Count the batts to confirm a full fill. The label coverage governs.
Trim Linear Footage and Miters - Trim = (perimeter - door openings) x (1 + waste%), pieces = ceil(net/stock); corners are 45-deg miters (base/casing) or a crown compound cut. 70 ft perimeter, 6 ft openings, 10% waste, 16 ft stock -> 70.4 ft, 5 sticks; a 38-deg crown corner is ~31.6 miter / 33.9 bevel cut flat. Verify on a scrap.
Allowable Building Area per Story (IBC Chapter 5) - The first feasibility number on a commercial project: how many square feet per floor the building may be, Aa = At + NS x If, where the frontage increase If = [F/P - 0.25] x W/30 rewards perimeter on open space and floors at zero below a quarter of the perimeter. The tabular areas come from Table 506.2 in the correct sprinkler column, and adding a sprinkler system can triple the area for a single-story building - the first lever a developer reaches for when the area is tight. A feasibility aid, not a code-official determination.
Egress Travel Distance, Common Path, and Dead-End Check (IBC Chapter 10) - The three distances a plans examiner checks against the floor plan: the exit-access travel distance to the nearest exit (Table 1017.2), the common path of egress travel before two independent paths are available (1006.2.1), and the longest dead-end corridor (1020.5). Each has its own editable limit that depends on the occupancy and whether the building is sprinklered; a single fail (e.g. travel over the limit) fails the floor, and a sprinkler system often clears it at once. A design aid, not a code-official determination.
Exterior Wall Opening Limit by Fire Separation Distance (IBC Table 705.8) - How much of an exterior wall may be windows and doors, capped as a percentage of the wall area by the fire separation distance and by whether the openings are protected or the building sprinklered. A wall under 3 ft from the line gets none; at 5 to 10 ft a sprinklered wall may be 25% glass; at 30 ft or more there is no limit. The distance to the lot line, not the facade design, sets the glass - one of the strongest arguments for a sprinkler system on a wall tight to the property line. A design aid, not a code-official determination.
Wood Bending Member (NDS Beam Stability Factor CL and Adjusted Fb') - Whether a wood beam bends without buckling its unbraced compression edge sideways, the flexural twin of the wood column check. Form the beam slenderness RB = sqrt(le x d / b^2), the critical buckling value FbE = 1.20 Emin' / RB^2, and the NDS 3.3.3 beam stability factor CL, then the adjusted bending value Fb' = Fb* x CL and the allowable moment M' = Fb' x S. A stocky, nearly-braced 4x12 keeps CL near 1.0; leaving the same beam tall and unbraced drops it off a cliff. A design aid, not a substitute for the engineer of record.
Glulam Volume Factor Cv (NDS 5.3.6) - The volume factor that reduces a glued-laminated beam's bending strength -- the glulam-specific penalty that the sawn-lumber CL check never applies. Cv = KL x (21/L)^(1/x) x (12/d)^(1/x) x (5.125/b)^(1/x), capped at 1.0, with L the span (ft), d and b the depth and width (in), x = 10 for softwoods (20 for Southern Pine), because a larger stressed volume is more likely to contain a strength-limiting defect. A 5-1/8 x 18 in glulam over 20 ft gives Cv = 0.965 (a 3.5% cut); a 6-3/4 x 24 in girder over 32 ft gives 0.870 (13%). The allowable bending uses the lesser of Cv and the beam-stability factor CL. A design aid, not a substitute for the engineer of record.
Wood Bending Member Shear (fv and the NDS Tension-Side End-Notch Reduction) - The end shear a wood beam carries, and how much a tension-side notch at the support takes away: the un-notched allowable Vr = (2/3) Fv' b d, the notched allowable V' = (2/3) Fv' b dn (dn/d)^2, and the actual stress fv = 3V / (2 b dn) on the net section. A single 2 in notch in a 4x12 cuts the allowable end reaction nearly in half - the reason the NDS penalizes notches on the tension side so hard. A design aid, not a substitute for the engineer of record.
Single-Shear Bolted / Dowel Lateral Design Value (NDS Yield-Limit Z) - How much lateral load one bolt through two wood members carries, from the NDS European yield model: all six single-shear yield modes (Im, Is, II, IIIm, IIIs, IV) computed from the dowel bearing strengths, the bolt bending yield, and the geometry, with the governing Z the smallest. A 1/2 in bolt into a thin side member almost always governs in mode IIIs. The reference value before the CD / CM / Cg / geometry adjustment factors, which the user applies. A design aid, not a substitute for the engineer of record.
Steel Beam Flexural Capacity (AISC 360 Ch. F, Compact + Braced) - Whether a compact, laterally-braced steel W-shape carries the moment: Mn = Mp = Fy x Zx, with the ASD allowable Mn/1.67 and the LRFD design 0.90 Mn. A W18x50 in A992 reaches 421 kip-ft nominal, 252 allowable, 379 design - the numbers a detailer reads off AISC Manual Table 3-2. The shape (Zx), not the grade, sizes the beam: the same steel in a section a fifth the weight carries barely a third of the moment. Compact + braced plastic plateau only (no LTB or slender-element reductions). A design aid, not a substitute for the engineer of record.
Required Plastic Section Modulus for a Steel Beam - The design inverse of the flexural-capacity check: enter the demand moment and Fy, get the plastic section modulus Zx to pick a W-shape. LRFD Zx >= 12 Mu/(0.90 Fy); ASD Zx >= 12(1.67)Ma/Fy (AISC 360 Ch. F, Mp = Fy Zx, inverted). A 200 kip-ft LRFD demand on 50 ksi steel needs Zx 53.3 in^3 (a W16x31 works); design it by ASD and the required Zx jumps to 80.2. Feeds straight back into the flexural-capacity tile. Compact, fully braced (Lb <= Lp); the shape lookup and the engineer of record govern.
Steel Beam Web Shear Capacity (AISC 360 Ch. G) - The web shear a steel beam carries at its ends, where the reaction is highest and the moment is zero: Vn = 0.6 x Fy x Aw x Cv1 with Aw = d x tw. For a rolled I-shape with a stocky web (h/tw under ~53.9 at Fy 50), Cv1 = 1.0 and the factors are Omega 1.50 / phi 1.00. A W18x50 carries 192 kips nominal, 128 allowable. Short heavily-loaded spans and coped ends are governed by the web, not the flange. Block shear at a coped end is a separate check. A design aid, not a substitute for the engineer of record.
Steel Column Compressive Capacity (AISC 360 Ch. E, Flexural Buckling) - The axial load a steel column carries, set by its slenderness not its area: KL/r, the elastic buckling stress Fe = pi^2 E / (KL/r)^2, and Fcr from the inelastic 0.658^(Fy/Fe) Fy or the elastic 0.877 Fe branch at the 4.71 sqrt(E/Fy) transition. A 14 ft W10x45 carries 239 kips allowable; stretch it to 24 ft and slenderness alone cuts it to 97 kips. The unbraced length is the number to watch. Flexural buckling only. A design aid, not a substitute for the engineer of record.
Eccentric Bolt Group in Shear (Elastic Vector Method) - The force on the worst bolt in a bracket or shear-tab group loaded off its centroid: the direct shear P/n superposed with the torsional shear from M = P x e, distributed by the group polar moment Ip = sum(x^2 + y^2). A 2x3 group at 3 in spacing under 30 kips at 6 in eccentricity puts 15.1 kips on the corner bolt; walk the load out to 12 in and torsion drives it to 27 kips. The conservative traditional method (not the instantaneous-center). Compare the resultant to the per-bolt strength. A design aid, not a substitute for the engineer of record.
Bolt Shear + Bearing / Tearout Strength (AISC 360 J3) - The design strength of one bolt through a plate, the smaller of shear rupture (Rn = ns x Fnv x Ab) and bearing/tearout at the hole (1.2 lc t Fu, capped at 2.4 d t Fu). A 3/4 in A325-N bolt in single shear through 1/2 in A36 gives 17.9 kip design (LRFD) / 11.9 kip allowable - bolt-shear-governed. Thin the plate to 1/4 in and tearout takes over at 14.3 kip: the flip this tile exists to catch. Standard holes, one bolt at one hole. A design aid, not a substitute for the engineer of record.
Column Base Plate under Axial Load (AISC Design Guide 1) - The plan size and thickness of a concentrically-loaded column base plate: the required concrete bearing area A1_req = Pu / (0.65 x 0.85 x f'c), the cantilever dimensions m, n, and n', and the thickness tp = l x sqrt(2 Pu / (0.90 Fy B N)). A W10x49 at 400 kips on a 14 in square A36 plate over 4 ksi concrete needs a 1-1/8 in plate; raise the load to 700 kips and the tile flags the plate as too small in bearing. Concentric axial only; anchor rods and shear transfer are separate. A design aid, not a substitute for the engineer of record.
Composite Shear Stud Strength and Count (AISC 360-22 I8) - Qn = 0.5 Asc sqrt(f'c Ec) <= Rg Rp Asc Fu, studs each side = V'/Qn. A 3/4 in stud, f'c 4000, Ec 3.64e6, Fu 65, Rg 1.0, Rp 0.75 -> Qn_calc 26.7, cap 21.6 kip governs; V' 400 -> 19 studs; a weak-position Rp 0.6 raises it to 24. Deck orientation and stud position matter. The engineer of record governs.
Composite Beam Flexural Strength (AISC 360-22 I3) - PNA-in-slab composite moment: C = As Fy, a = C/(0.85 f'c be), Mn = C(d/2 + tslab - a/2), phi Mn = 0.90 Mn. As 8.0, Fy 50, d 16, slab 4, be 90, f'c 4 -> C 400 kip, a 1.31 in, phi Mn 340 kip-ft; a narrow be 24 pushes a past the slab and flags PNA-in-steel. The engineer of record governs.
Steel Beam Camber from Dead-Load Deflection - Camber = a fraction (75-80%) of the dead-load deflection 5 w L^4 / (384 E I), rounded to 1/4 in. 1.0 kip/ft, 40 ft, I 2100 -> 0.95 in deflection, 3/4 in camber; a stiff 20 ft beam deflecting 0.05 in is left flat (below the ~3/4 in practical minimum). The structural drawings govern.
Steel Floor Walking Vibration (AISC DG11) - AISC Design Guide 11 walking-vibration check: peak acceleration ap/g = P0 e^(-0.35 fn) / (beta W) against the occupancy limit (0.5% office/residence, 1.5% mall). Stiffer is not automatically better -- low-frequency floors (4-8 Hz) resonate with the walking harmonic. The serviceability check strength alone misses.
Column Web Panel-Zone Shear (AISC 360 J10.6) - The AISC 360-16 J10.6 panel-zone shear strength of a moment-connection column web, both branches: basic Rn = 0.60 Fy dc tw (J10-9) and the flange-stiffened bonus (J10-11, allowed only when panel-zone deformation is in the analysis), against the joint demand, with a doubler-plate flag. The moment-frame joint often fails here first.
Panel-Zone Shear Under High Column Axial (AISC 360 J10-10/J10-12) - The axial reduction steel-panel-zone-shear flags but does not carry: past Pr = 0.4 Pc the basic panel-zone strength takes (1.4 - Pr/Pc) (Eq. J10-10), past 0.75 Pc the deformation-modeled strength takes (1.9 - 1.2 Pr/Pc) (Eq. J10-12), Pc = Py = Fy Ag. A W14-class column at 45% of axial yield loses 5% of its panel zone; at 83% it is losing 1.2% per additional percent of axial. Below the thresholds it matches the sibling exactly. A design aid, not a connection design.
Panel-Zone Doubler-Plate Thickness (AISC 360 J10.6) - The how-thick that steel-panel-zone-shear leaves open: when the panel-zone check fails, the doubler plate is sized by two limits. Strength t = (Vu - phiRn_bare) / (0.90 x 0.60 Fy dc); stability (Eq. J10-12) t >= (dz + wz)/90 for a plate not plug-welded to the web. On a stocky column with a small shortfall the stability minimum governs (a strength-only calc would spec a plate too thin to be stable); on a deep beam the strength governs. Reports the governing thickness rounded up to the next 1/16-in plate. A detailing aid, not a stamped connection design.
Reinforced Concrete Beam Flexural Capacity (ACI 318-19) - The design moment of a singly-reinforced, tension-controlled rectangular concrete beam: the equivalent stress-block depth a = As x fy / (0.85 x f'c x b), the nominal moment Mn = As x fy x (d - a/2), and phi Mn with phi = 0.90, plus the demand/capacity ratio against an entered required moment. A 12 x 24 in beam with three #9 Grade 60 bars on 4,000 psi concrete develops 260 kip-ft -- the textbook value -- and carries a 200 kip-ft demand at 77% utilization. Singly-reinforced and assumed tension-controlled (confirm epsilon_t >= 0.005); compression steel, T-beam action, and minimum steel are separate checks. A design aid, not a substitute for a licensed engineer's design.
Reinforced Concrete Beam Shear and Stirrup Spacing (ACI 318-19) - Whether a rectangular concrete beam carries its shear and what stirrup spacing it needs: the simplified concrete contribution Vc = 2 x lambda x sqrt(f'c) x bw x d, the design phi Vc at phi = 0.75, the stirrup demand Vs = Vu/phi - Vc when the demand exceeds phi Vc, the required spacing s = Av x fyt x d / Vs, and the d/2 code maximum. A 12 x 21.5 in beam on 4,000 psi concrete carries 24.5 kip on concrete alone; a 40 kip demand needs #3 stirrups at 10 in (the d/2 cap governs over the computed 13.7 in). Uses the simplified Vc for a member without axial load; the section upper limit and minimum-reinforcement triggers are separate checks. A design aid, not a substitute for a licensed engineer's design.
Concrete Threshold and Cracking Torsion (ACI 318-19 22.7) - The two torsion thresholds every spandrel and edge beam is checked against: torsion may be neglected when the factored torque is below phi x Tth, where the threshold torsion Tth = lambda x sqrt(f'c) x (Acp^2/pcp) with Acp = b x h the outside area and pcp = 2(b+h) the outside perimeter; the section cracks in torsion at Tcr = 4 x Tth (phi = 0.75). A 12 x 20 in beam on 4,000 psi concrete has Tth = 4.74 ft-kip, so torsion is ignored below 3.56 ft-kip and the section cracks at 18.97 ft-kip; an 18 x 24 in beam raises the threshold to 11.7 ft-kip -- torsion capacity grows fast with section size. Above phi x Tth closed stirrups and longitudinal steel must be designed. A design aid, not a substitute for a licensed engineer's design.
Rebar Tension Development Length (ACI 318-19) - The straight-bar tension development length from the ACI 318-19 general equation: ld = (3/40) x fy x psi_t x psi_e x psi_s x psi_g / (lambda x sqrt(f'c) x (cb + Ktr)/db) x db, with the confinement term capped at 2.5, the psi_t x psi_e product capped at 1.7, and the 12 in floor. A #8 Grade 60 bottom bar in 4,000 psi concrete, well confined, develops in 28.5 in; cast as a top bar the 1.3 casting-position factor stretches it to 37 in -- the trap the 40-bar-diameter rule of thumb papers over. Straight-bar tension only; hooks, compression bars, and lap splices are separate checks. A design aid, not a substitute for a licensed engineer's detailing.
Shallow Foundation Bearing Capacity (Vesic) - The gross ultimate and allowable bearing pressure of a shallow footing from the soil's own strength: qu = c x Nc + q x Nq + 0.5 x gamma x B x Ngamma with the Vesic bearing-capacity factors from the friction angle, De Beer / Vesic shape factors for square and circular footings, and the customary factor of safety of 3. A 6 ft strip footing 4 ft deep on a phi = 32 medium-dense sand carries 22 ksf ultimate, 7.3 ksf allowable -- the number the footing-area tile has always needed handed to it; a phi = 0 stiff clay pins the Prandtl Nc = 5.14 branch. General shear on a level, concentric footing with deep groundwater; settlement usually governs on sand and is separate. A design aid, not a substitute for a geotechnical engineer's report.
Lateral Earth Pressure and Thrust (Rankine) - The push of retained soil: the Rankine active coefficient Ka = tan^2(45 - phi/2) and passive Kp = 1/Ka, the triangular active thrust Pa = 0.5 x Ka x gamma x H^2 at H/3, the rectangular surcharge term Ka x q x H at H/2, the combined resultant and its height, and the passive resistance. A 10 ft wall of phi = 30 sand carries exactly 2,000 lb/ft active against 18,000 lb/ft passive -- the 9:1 ratio that is why passive is never counted on lightly; a 250 psf parking surcharge grows the thrust 42% and lifts its arm. Cohesionless, vertical, frictionless, dry Rankine case only. A design aid, not a substitute for a geotechnical engineer's report.
At-Rest Earth Pressure on a Braced Wall (Jaky K0) - The push of retained soil on a wall that cannot yield -- a basement wall, a braced excavation, a rigid box culvert -- where the Rankine active pressure does not apply because the soil never relaxes to its active limit: Jaky's K0 = 1 - sin phi, the triangular at-rest thrust P0 = 0.5 x K0 x gamma x H^2 at H/3, the uniform-surcharge term K0 x q x H at H/2, the combined resultant and its height. A 10 ft wall of phi = 30 sand carries 3,000 lb/ft at rest against only 2,000 lb/ft active -- exactly 1.5x more, the error a designer makes reaching for the active tile on a braced wall. Normally-consolidated cohesionless, dry; an overconsolidated or submerged case needs its own analysis. A design aid, not a substitute for a geotechnical engineer's report.
Submerged-Backfill Earth Pressure (Buoyant + Hydrostatic) - The push of a backfill below the water table, where the dry Rankine tile no longer applies: the soil skeleton pushes with its buoyant weight (gamma_sat - 62.4) at the Ka reduction, but the water pushes with the full hydrostatic pressure at no reduction. Pa' = 0.5 x Ka x gamma_buoy x H^2, Pw = 0.5 x 62.4 x H^2, plus the Ka q H surcharge. A 10 ft phi = 30, 125 pcf sand pushes 2,083 lb/ft dry but 4,163 lb/ft submerged -- almost exactly 2x, and three-quarters of it is water, which is why a working drain is the cheapest structural element on the wall. Fully-submerged active case. A design aid, not a substitute for a geotechnical engineer's report.
Sloped-Backfill Earth Pressure (Rankine Inclined Surface) - The push of a backfill that rises behind the wall at a slope beta, which the level Ka under-predicts: the Rankine inclined-surface coefficient Ka = cos b (cos b - sqrt(cos^2 b - cos^2 phi)) / (cos b + sqrt(cos^2 b - cos^2 phi)), the thrust Pa = 0.5 x Ka x gamma x H^2 acting parallel to the slope, and its horizontal (overturning) and vertical (heel) components. A 15 deg backfill on a phi = 30 sand raises Ka from 0.333 to 0.373 -- a 12% heavier thrust that also tilts and adds an uplift the level analysis never sees; beta must stay below phi or the slope cannot be retained on Rankine terms. Cohesionless, vertical wall face. A design aid, not a substitute for a geotechnical engineer's report.
Coulomb Active Earth Pressure (Wall Friction and Batter) - The active thrust Rankine leaves on the table: Coulomb credits wall friction delta, a battered face theta, and a sloped backfill alpha, Ka = cos^2(phi - theta) / [cos^2(theta) cos(delta + theta) (1 + sqrt(sin(phi + delta) sin(phi - alpha) / (cos(delta + theta) cos(theta - alpha))))^2]. A rough vertical wall on a phi = 30 level backfill carries only 1,676 lb/ft of horizontal thrust once two-thirds-phi wall friction is credited, versus 2,000 lb/ft by Rankine -- a 16% cut in the overturning force plus a downward drag that resists sliding. Reduces exactly to Rankine when the wall is smooth, vertical, and the fill level. Cohesionless, active limit. A design aid, not a substitute for a geotechnical engineer's report.
Cantilever Retaining Wall Stability (Overturning / Sliding / Bearing) - The three global-stability checks of a cast-in-place cantilever retaining wall: the restoring moments of the stem, base, and heel soil about the toe against the Rankine thrust's overturning moment, the base friction against sliding (both against the IBC 1807.2.3 minimum of 1.5), and the eccentricity-based toe / heel bearing pressures with a middle-third check. A 10 ft wall on a 6 ft base passes dry at 3.37 / 1.69 / 1,731 psf toe -- and the same wall fails sliding at 1.31 under a 300 psf surcharge, the case that most often governs. Internal member design, passive toe credit, and seismic pressure are separate. A design aid, not a substitute for a licensed engineer's design.
Consolidation Time Rate (Terzaghi) - Terzaghi 1-D consolidation: Tv = (pi/4)(U/100)^2 for U <= 60% else 1.781 - 0.933 log10(100-U), time t = Tv Hdr^2/cv. U 90%, cv 0.1 ft^2/day, Hdr 10 ft -> Tv 0.848, 848 days; U 50% -> 196 days (the decelerating curve). Hdr is half the layer for double drainage (a 4x time swing). The engineer of record governs.
SPT Allowable Bearing on Sand (Meyerhof) - Meyerhof settlement-controlled allowable from the SPT N60: qa = N60/4 ksf for B <= 4 ft else (N60/6)((B+1)/B)^2, times Kd = min(1 + 0.33 D/B, 1.33). N60 20, B 6, D 2 -> 4.54 base, Kd 1.11, 5.04 ksf; a 3 ft footing gives 5.00 ksf. A 1 in settlement allowable, not the ultimate; N60 energy-corrected. The geotechnical report governs.
Liquefaction Triggering Screening (Seed-Idriss CSR) - Seed-Idriss screen: rd = 1 - 0.00233172 z (z <= 30.02 ft; per-meter 0.00765/0.0267 scaled by 0.3048), CSR = 0.65 amax (sv/s'v) rd, FS = (CRR/CSR) MSF, liquefiable if FS < 1. amax 0.30g, sv 2000, s'v 1200 psf, z 16.4 ft, CRR 0.20 -> CSR 0.313, FS 0.64, liquefiable; denser sand (CRR 0.40) -> FS 1.28. A level-ground screen; the geotechnical engineer of record governs.
Pile Group Efficiency (Converse-Labarre) - Why a pile group carries less than the sum of its piles: the stress bulbs of adjacent piles overlap, so the Converse-Labarre efficiency Eg = 1 - theta((n-1)m + (m-1)n)/(90 m n) with theta = atan(d/s) discounts the group. A 3x3 group of 12 in piles at 3d = 36 in spacing (100 kip each) runs Eg = 0.727 -> 654 kip, not the 900 kip the naive sum implies; squeeze to 2d = 24 in and Eg falls to 0.606 -> 546 kip, losing another 108 kip for zero added piles. Below about 3d, efficiency drops under 0.7, so close-spaced piles give diminishing returns. An empirical friction-pile hand check; block failure and settlement are separate. A design aid; the geotechnical engineer of record governs.
Reinforced CMU Wall Out-of-Plane Flexure (TMS 402 ASD) - The allowable out-of-plane bending moment of a reinforced, fully grouted CMU wall by the working-stress cracked transformed-section method: the modular ratio n = Es/(900 f'm), the neutral-axis and lever-arm coefficients k and j, the steel-governed Ms = As Fs j d against the masonry-governed Mm = 0.5 Fb k j b d^2, and whichever is less governs. An 8 in wall with #5 bars at 24 in on 2,000 psi masonry carries 1,428 lb-ft per foot, steel-governed -- the textbook lightly-reinforced outcome; tighten the bars to 16 in and the masonry compression block takes over at 1,924. Cracked section, pure flexure, no axial interaction or one-third increase. A design aid, not a substitute for the engineer of record's stamped design.
Masonry Headed Anchor Bolt Tension (TMS 402 ASD) - The allowable tension of a headed anchor bolt in grouted masonry -- the anchor that fastens a ledger or sill to a CMU wall, which the wall-design tiles never check. TMS 402 allowable-stress design takes the lesser of masonry breakout Bab = 1.25 x Apt x sqrt(f'm), with Apt = pi x lbe^2 the projected breakout cone, and steel Bas = 0.6 x Ab x fy. A 3/4 in anchor (Ab = 0.442 in^2, Fy 36 ksi) embedded 4 in in 1,500 psi masonry gives Bab = 2,433 lb and Bas = 9,547 lb, so masonry breakout governs at 2,433 lb; double the embedment to 8 in and Bab rises to 9,733 lb, so now the 9,547 lb steel governs. Edge distance reduces Apt; shear (pryout) is a separate check. A design aid, not a substitute for the engineer of record's stamped design.
Reinforced CMU Shear Wall In-Plane Shear (TMS 402 ASD) - The allowable in-plane shear of a reinforced, fully grouted masonry shear wall: the masonry term Fvm = 0.5 x ((4.0 - 1.75 M/(V dv)) sqrt(f'm)) + 0.25 P/An that grows with axial compression and shrinks with slenderness, the horizontal-steel term Fvs = 0.5 Av Fs dv/(An s), and the combined stress against the shear-span-graded 3-to-2 sqrt(f'm) cap, times the net area for the allowable force. An 8 in by 8 ft wall under 20 kip of axial with #4 horizontals at 48 in carries 76 psi and 55.7 kip -- the capacity the seismic-base-shear demand is checked against. Sustained axial only; special-reinforced detailing is separate. A design aid, not a substitute for the engineer of record's stamped lateral design.
Reinforced CMU Wall Axial Compression (TMS 402 ASD) - The allowable concentric axial load of a reinforced masonry wall or column: the material capacity 0.25 f'm An + 0.65 Ast Fs (the steel term for laterally tied bars) times the slenderness factor -- 1 - (h/140r)^2 up to h/r = 99 and the Euler-type (70r/h)^2 beyond, the two branches meeting continuously. A one-foot strip of a 12 ft, 8 in grouted wall with #5 verticals at 24 in carries 38.3 kip; stretch it to 24 ft and the slender branch cuts it to 14.0 kip, the buckling penalty that forces thickness or a brace. Pure axial; the moment interaction pairs with the flexure tile. A design aid, not a substitute for the engineer of record's stamped design.
Masonry Wall Dead Load - Wall dead load = hollow (NCMA) weight + grout adder prorated by grout spacing (capped at full). 8 in CMU, grouted 48 in o.c. -> 59.8 psf (598 lb/ft at 10 ft); fully grouted -> 84 psf, a 40% heavier wall. Line load and total from height/area. The NCMA tables and engineer of record govern.
Brick Veneer Anchor Spacing and Count (TMS 402 / IBC 1405) - Anchor count = ceil(area / area-per-anchor) with the 32 in horizontal / 24 in vertical spacing caps, per TMS 402 / IBC 1405. A 200 ft^2 veneer at 2.67 ft^2/anchor -> 75 ties; a high-wind 2.0 ft^2 limit -> 100. TMS 402 / IBC and the engineer of record govern.
Masonry Lintel Arching Load (Triangular Load Over an Opening) - The triangular dead load a lintel carries within a 45-degree triangle (height span/2) when the wall above >= span/2, else the full rectangle. A 6 ft opening, 60 psf, 5 ft above -> 540 lb (90 lb/ft); only 2 ft above -> the full 720 lb. Dead load only; the engineer of record governs.
Wood Diaphragm Unit Shear and Chord Force (SDPWS) - The flexible wood diaphragm as a deep horizontal beam: the end reaction V = wL/2, the maximum unit shear v = wL/(2b) the sheathing nailing must carry, the moment wL^2/8, and the chord force T = C = M/b the perimeter members resolve it into. A 192 x 120 ft roof at 516 plf runs 413 plf of unit shear -- the published WoodWorks value -- and 19.8 kip of chord force; narrow the diaphragm to 60 ft and both exactly double. Simple-span flexible (tributary) distribution; collectors, deflection, and openings are separate. A design aid, not a substitute for the engineer of record's stamped lateral design.
Wood Shear Wall Unit Shear and Holdown (SDPWS / ASD) - The two numbers a wood shear wall is detailed for: the unit shear v = V/b checked against the SDPWS nailing schedule, and the net holdown tension T = (V h - 0.6 W b/2)/b once the story shear tries to overturn the wall and only 0.6 times the tributary dead load resists it (the ASD combination). An 8 ft wall taking 8 kip at 10 ft with 3,000 lb of dead load runs 1,000 plf and a 9.1 kip holdown; load the wall to 20,000 lb and gravity cuts the holdown to 4.0 kip, and past the balance point the tile clamps to zero. Segmented wall; sill anchorage and chord bearing are separate. A design aid, not a substitute for the engineer of record's stamped lateral design.
Wood Shear Wall Deflection (SDPWS Eq 4.3-1) - How far the top of a wood shear wall drifts, from the SDPWS three-term equation: end-post bending 8vh^3/(EAb), panel shear plus nail slip vh/(1000 Ga) with the tabulated apparent stiffness, and anchorage rotation h da/b from the holdown slack -- in the equation's own calibrated units. A 10 x 8 ft wall at 400 plf on 4x4 posts deflects 0.47 in (0.40% drift), the shear and anchorage terms carrying nearly all of it; double the height and the h^3 bending term wakes up. Checked against the ASCE 7 story-drift limit -- the reason a tall narrow wall can pass strength and fail stiffness. A design aid, not a substitute for the engineer of record's stamped lateral design.
Collector / Drag Strut Axial Force (ASCE 7 12.10) - The accumulated axial force in a collector (drag strut) that gathers diaphragm shear across an opening and drags it back to the shear wall: collector_force = unit_shear x collector_length, plus the ASCE 7 12.10.2.1 Omega0 overstrength demand the diaphragm chord never carries. The separate load path diaphragm-shear leaves out.