concrete beam for combined shear and torsion per ACI 318-19M.xlsx

This calculation determines the required transverse and longitudinal torsion reinforcement for a rectangular reinforced concrete beam subjected to combined shear and torsion, in accordance with ACI 318-19M — Building Code Requirements for Structural Concrete (Metric).

Scope

• Rectangular, solid, non-prestressed beams
• Normal-weight or lightweight concrete (via λ factor)
• Combined factored shear (V_u) and factored torsion (T_u)
• No applied axial load
• Strut angle θ = 45° (default for non-prestressed members per ACI 22.7.6.1.2)

What the sheet calculates

1. Section properties — A_cp, p_cp, A_oh, p_h, A_o
2. Torsion threshold check (ACI Table 22.7.5.1, 22.7.4.1(a)) — cracking torsion T_cr, threshold torsion T_th, and decision logic for whether torsion may be neglected, minimum reinforcement only, or full design
3. Concrete shear capacity V_c (ACI Table 22.5.5.1)
4. Cross-sectional adequacy against diagonal strut crushing (ACI Eq. 22.7.7.1(a))
5. Transverse reinforcement — torsion stirrups A_t/s, shear stirrups A_v/s, minimum (A_v+2A_t)/s (ACI 9.6.4.2), maximum stirrup spacing (ACI 9.7.6.3.3)
6. Longitudinal torsion reinforcement — required A_l from equilibrium, minimum A_l per ACI 9.6.4.3, governing bar count (with corner-bar minimum per ACI 9.7.5.1)
7. Utilisation summary with Pass/Fail indicators for the three governing limit states

Features

• Built on the XLC CalcSheet template with section numbering, calculation status block, and @EQS rendered equations in column G
• Consistent units throughout via the workbook unit selector (Calc1!E14) — switch between SI (mm) and other unit systems and all named unit formulas update automatically
• Input cells highlighted in light blue; calculated cells locked
• OVD()/UND() fractions used for genuine engineering divisions so equations render as displayed fractions matching the code book layout
• Inline notes with ACI clause references on every key formula

Validation

The workbook contains a dedicated validation sheet — Validation - MacGregor 7-6 — which loads the inputs from MacGregor & Wight, Reinforced Concrete: Mechanics and Design, Example 7-6, and provides a side-by-side comparison panel showing this sheet's output against the textbook's published values for 20 quantities (geometry, T_cr, T_th, V_c, combined stress, A_t/s, A_v/s, s_max, A_l, A_l,min). Deltas update live with the calculation, so any future edit re-runs the regression check automatically.

Required inputs

• Beam geometry: overall depth h, width b, cover to stirrup centreline r
• Materials: f'_c, f_y, λ (concrete weight factor)
• Loading: factored torsion T_u, factored shear V_u
• Design parameters: φ, θ, longitudinal bar diameter d_b

Outputs

• Required (A_v+2A_t)/s and maximum stirrup spacing s_max
• Required longitudinal torsion steel area and number of bars
• Pass/Fail check for cross-section adequacy against strut crushing
• Pass/Fail check on longitudinal steel provided vs. required

Limitations

• Solid sections only (A_o = 0.85·A_oh); not suitable for hollow sections without modification
• Non-prestressed members only
• No axial load combination
• Stirrup detailing (anchorage, hook geometry) is not part of the calculation — designer to verify per ACI 25.7

References

• ACI 318-19M — Building Code Requirements for Structural Concrete (Metric)
• ACI 445.1R-12 — Report on Torsion in Structural Concrete
• MacGregor, J.G. & Wight, J.K., Reinforced Concrete: Mechanics and Design, Pearson
• Lampert & Thürlimann — thin-walled tube / space truss analogy

Requires the XLC add-in for rendered equations in column G and named unit formulas. Without XLC, all numerical results still calculate correctly — only the equation rendering and unit labels are affected.