T-Beam Flexural Capacity (ACI 318-19)

Which of two behaviors applies is the whole question: if the trial stress block a = As fy / (0.85 f'c be) stays inside the slab -- the usual case for positive moment -- the section is just a rectangle be wide and the web width never enters the answer. Only when it runs past does the section become a true T, splitting into a flange couple Asf = 0.85 f'c (be - bw) hf / fy at lever arm d - hf/2 and a web couple for the rest. A 12 in web with a 3 in slab, 36 in effective width, 8 sq in of steel at d = 24 develops 872.9 kip-ft; treating it as a plain rectangle 36 in wide returns 881.6, about 1% UNCONSERVATIVE. Effective width uses the same shared 6.3.2 routine, so the two cannot disagree, with an override for a be off the drawings. POSITIVE MOMENT ONLY -- over a support the slab is in tension and the section reverts to a rectangle of the web width.

trial a = As fy / (0.85 f'c be); if a <= hf the section is rectangular of width be and Mn = As fy (d - a/2); if a > hf then Asf = 0.85 f'c (be - bw) hf / fy, Asw = As - Asf, a = Asw fy / (0.85 f'c bw), and Mn = Asf fy (d - hf/2) + Asw fy (d - a/2). c = a/beta1; eps_t = 0.003 (d - c)/c; phi = 0.90 at eps_t >= eps_ty + 0.003, 0.65 at eps_t <= eps_ty = fy/Es, interpolated between.

ACI 318-19: 22.2.2.4.1 equivalent rectangular stress block, 22.2.2.4.3 beta1, 6.3.2 effective flange width (delegated to the landed t-beam-effective-flange-width tile rather than reimplemented), and 21.2.2 strength-reduction factor.

The T-beam flexural derivation is standard reinforced-concrete mechanics reproduced in every textbook and in free university course notes; the code sections are cited by number and no table is reproduced.

Estimate. AHJ and licensed professional govern.

Field names used by the API: fc_psi, fy_psi, as_in2, bw_in, hf_in, d_in, ln_in, sw_in, beam_type, mu_kipft, be_in, a_trial_in, asf_in2, asw_in2, a_in, mn_kipft, phi_mn_kipft, eps_t, phi, util

• Behavior test trial a on width be against hf decides rectangular versus true TACI 318-19 22.2.2.4.1
• Flange couple Asf = 0.85 f'c (be - bw) hf / fy at lever arm d - hf/2standard T-beam resolution
• Effective width delegated to computeTBeamEffectiveFlangeWidth (6.3.2), with an overrideACI 318-19 6.3.2
• phi 21.2.2, tension-controlled at eps_ty + 0.003, not the 318-14 fixed 0.005ACI 318-19 21.2.2
• Positive moment only at a support the flange is in tension and the section is a web-width rectanglestated scope limit
• Singly reinforced compression steel, minimum steel, shear, deflection, and development are separatestated scope limit