Staggered-Hole Net Width (AISC 360 B4.3b)
The net width of a tension member across a STAGGERED (zigzag) bolt chain.
Example
You enter
- Gross plate width (in) 12
- Plate thickness (in) 0.5
- Bolt diameter (in) 0.75
- Hole allowance over the bolt diameter (in) 0.125
- Gage, transverse spacing between gage lines (in) 3
- Pitch, longitudinal spacing between staggered holes (in) 2
- Holes crossed by the straight chain 2
- Holes crossed by the zigzag chain 3
- Gage spaces crossed by the zigzag chain 2
You get
- Hole deducted 0.875
- Straight chain 10.250 in net width
- Net width zigzag (in) 10.0417
- Stagger credit (in) 0.666667
- Net area (in²) 5.02083
- Pitch where straight governs (in) 2.29129
Details, formula, and sources
B4.3b deducts the diameters of ALL holes in a diagonal chain and then ADDS s^2/4g for each gage space it crosses, and every possible chain has to be checked with the SMALLEST net width governing. Two things get missed: the hole comes off at the bolt diameter plus 1/8 in, not the bolt diameter, which overstates the area on every hole in the chain; and staggering has a CEILING -- past a computable pitch the straight chain governs and further stagger buys nothing at all. It reports that pitch, the number worth having before the pattern gets redrawn.
hole diameter deducted = bolt diameter + allowance (1/8 in default). Straight chain net width = W - n_straight x hole. Zigzag chain net width = W - n_zigzag x hole + k x s^2/(4g), k gage spaces crossed. The smaller governs; An = governing net width x thickness. The pitch at which the two chains are equal is s = sqrt(4 g (n_zigzag - n_straight) x hole / k).
AISC 360 Section B4.3b (Net Area).
AISC 360 is published as a free PDF download by the American Institute of Steel Construction.
Estimate. AHJ and licensed professional govern.
Field names used by the API: plate_width_in, thickness_in, bolt_dia_in, hole_allowance_in, gage_in, pitch_in, holes_straight, holes_zigzag, gage_spaces_zigzag, hole_dia_in, net_width_straight_in, net_width_zigzag_in, stagger_credit_in, net_area_in2, pitch_where_straight_governs_in
- Zigzag credit s^2/4g added for each gage space in the chainAISC 360 B4.3b
- Hole deduction bolt diameter + 1/8 in by default; editable for oversized and slotted holesAISC 360 B4.3b and Commentary
- Governing chain the smallest net width of all possible chains; only the two entered are evaluatedAISC 360 B4.3b
- Stagger ceiling pitch = sqrt(4 g (n_zigzag - n_straight) x hole / k), past which the straight chain governsderived from B4.3b
- Shape rectangular plate; angles use the developed flat width and are not coveredstated scope limit