Concrete beam

A nonprestressed reinforced concrete beam, rectangular or T-shaped, designed to ACI 318-19 (Chapters 9, 21, 22, 24 and 25) by strength design with the ASCE 7-22 load combinations. One model covers simple spans, cantilevers, overhangs and continuous beams; the factored moments and shear can also be entered directly.

Inputs of the concrete beam #

• Materials: f'c (at least 2,500 psi, 19.2.1.1), Grade 60 or 80 bars, normalweight or lightweight concrete (λ by Table 19.2.4.1(b), or from the equilibrium density wc by Table 19.2.4.1(a)), the modulus Ec by 19.2.2.1(b) (57,000√f'c) or 19.2.2.1(a) (wc^1.5 × 33√f'c, always used for lightweight concrete), and the stirrup grade. The stirrup yield strength used for shear and torsion is limited to 60 ksi (Table 20.2.2.4(a)).
• Section: web width bw and overall depth h. A T-beam adds the slab thickness hf and the effective flange width: from Table 6.3.2.1 (slab on both sides: overhang the least of 8hf, sw/2 and ℓn/8 each side; slab on one side: 6hf, sw/2 and ℓn/12) with the clear distance sw to the next web and the shortest clear span, or entered. An isolated T-beam uses the entered width and is checked against 6.3.2.2 (hf ≥ bw/2, bf ≤ 4bw). The clear cover to the stirrups (1.5 in. prefilled, Table 20.5.1.3.1) and the maximum aggregate size (for 25.2.1) complete the section.
• Reinforcement: bottom bars in one or two layers (the second layer one bar diameter or 1 in. clear above the first, 25.2.2), top bars, stirrups (size, legs, spacing) and the bar coating. The bars are taken as continuous over the beam; the top bars act as compression steel at positive moment and as tension steel at negative moment.
• Loads and supports: the beam length, pins or fixed supports anywhere, line and point loads per load type (see Loads and combinations) and the self-weight bw × h × the unit weight entered (150 pcf prefilled; the slab weight of a T-beam belongs in the line loads). The support width sets the face of the support; the shear is taken at d from the face when Design shear at d is ticked (9.4.3.2: the reaction compresses the end region and the loads act at or near the top). A point load between the face and d is detected and the face value is used instead. Instead of loads, the factored Mu+, Mu− and Vu at the critical sections can be entered with the clear span and its support condition.
• Torsion: the factored torsion Tu at the critical section (0 = none), whether it is equilibrium torsion (22.7.3.1) or compatibility torsion that may be reduced to φTcr (22.7.3.2), and the area of longitudinal torsion bars provided in addition to the flexural bars.
• Deflection: span / n for the immediate live load deflection (Table 24.2.2: 360 for floors, 180 for flat roofs) and for the deflection after attachment of nonstructural elements (480 where they are likely to be damaged, 240 otherwise), the sustained part of the live load and the load duration (ξ of Table 24.2.4.1.3). These are the engineer's choices; 0 turns a limit off.

Auto-design (editor toolbar) varies the bottom and top bars (size and count), stirrup size and spacing; width and depth when unlocked. Objectives: lowest cost index (concrete, formwork, reinforcement); least reinforcement; shallowest, then cost. Kept unless you select them: overall depth h, web width bw. Every other input is kept; see Auto-design.

Checks performed #

The diagrams show the loading, the section, the shear and moment of the combination that governs the positive moment, and the immediate deflection under the dead and live loads (with Ie of the critical span).

Limitations #

• Nonprestressed beams only; deep beams (clear span ℓn ≤ 4h between supports, 9.9.1.1) are reported as not feasible (design them by Chapter 23).
• The bars are continuous over the beam: cutoffs, bar development at the cutoffs (9.7.3) and the anchorage at the supports are left to the engineer (the development lengths are listed as an advisory).
• One effective depth d (to the bottom bars) is used for shear; ρw uses the smaller of the top and bottom steel where the beam has negative moment.
• Torsion: solid rectangular web with closed stirrups, θ = 45°; overhanging flanges are neglected in Acp and pcp (conservative for Tth and Tcr); the entered Tu is applied at the critical section for shear; all stirrup legs are taken to resist shear and the outer legs torsion. Hollow sections and prestressed members are not covered.
• Deflection: one Ie per span from the maximum positive service moment of that span (24.2.3.7), no deduction of the deflection that occurs before the nonstructural elements are attached, and the whole live load added after attachment (both conservative). The crack-control check uses fs = 2/3 fy.
• The tension-controlled requirement is applied as printed in 9.3.3.1 of the ACI 318-19 text on hand (εt ≥ εty + 0.003) [verify against the latest errata].
• Skin reinforcement and flange distribution of negative-moment bars (24.3.4) are advisories, not designed.

Verification examples #

The beam is verified against the free StructurePoint design examples (spBeam verification, written to ACI 318-14; the flexure, shear, torsion and spacing provisions used are unchanged in ACI 318-19) and against hand calculations in closed form derived step by step in the test file. ACI 318-19 replaced the Branson effective moment of inertia with the expression of Table 24.2.3.5, so the published 318-14 deflections are deviations (ACI318-14-IE: the program gives 5 to 16 % larger, more conservative, deflections; Mcr, Icr and Ig agree).

Hand calculations: