Beam Shear Capacity Calculator
Free Beam shear capacity Calculator for structural engineering projects. Enter dimensions to get material lists and cost estimates.
Formula
Vc = 2 * sqrt(fc) * bw * d | Vs = Av * fy * d / s | phi-Vn = 0.75 * (Vc + Vs)
The concrete shear contribution Vc uses ACI 318 simplified method with 2*sqrt(fc)*bw*d. The steel stirrup contribution Vs depends on stirrup area, yield strength, effective depth, and spacing. The total nominal shear strength Vn is multiplied by the shear reduction factor phi of 0.75 to obtain the design capacity.
Worked Examples
Example 1: Typical Rectangular Beam
Problem: A 12-inch wide beam has an effective depth of 20 inches, concrete strength of 4000 psi, and No. 3 stirrups (Av = 0.22 sq in) at 8-inch spacing with fy = 60,000 psi.
Solution: Vc = 2 * sqrt(4000) * 12 * 20 = 30,358 lb = 30.36 kips\nVs = 0.22 * 60000 * 20 / 8 = 33,000 lb = 33.00 kips\nVn = 30.36 + 33.00 = 63.36 kips\nphi-Vn = 0.75 * 63.36 = 47.52 kips
Result: Design shear capacity = 47.52 kips
Example 2: Deep Beam with Close Stirrups
Problem: A 16-inch wide beam with d = 30 inches, fc = 5000 psi, No. 4 stirrups (Av = 0.40 sq in) at 6-inch spacing, fy = 60,000 psi.
Solution: Vc = 2 * sqrt(5000) * 16 * 30 = 67,882 lb = 67.88 kips\nVs = 0.40 * 60000 * 30 / 6 = 120,000 lb = 120.00 kips\nphi-Vn = 0.75 * (67.88 + 120.00) = 140.91 kips
Result: Design shear capacity = 140.91 kips
Frequently Asked Questions
What is beam shear capacity and why does it matter?
Beam shear capacity is the maximum shear force a reinforced concrete beam can resist before failing in a diagonal tension mode. Shear failures are sudden and brittle, unlike flexural failures which show warning signs like cracking and deflection. The total shear capacity Vn equals the concrete contribution Vc plus the steel stirrup contribution Vs. Designing adequate shear reinforcement is critical for structural safety.
How is the concrete shear contribution Vc calculated?
According to ACI 318, the simplified concrete shear strength is Vc = 2 * sqrt(fc) * bw * d, where fc is the concrete compressive strength in psi, bw is the beam web width in inches, and d is the effective depth in inches. This formula assumes normal-weight concrete without axial load. The result is in pounds of force. For lightweight concrete, a lambda factor of 0.75 to 0.85 is applied as a multiplier.
What are stirrups and how do they resist shear?
Stirrups are U-shaped or closed-loop steel bars placed perpendicular to the longitudinal reinforcement in a beam. They intercept diagonal shear cracks and transfer the tensile forces across the crack back into the concrete. The steel shear contribution is Vs = Av * fy * d / s, where Av is the total cross-sectional area of stirrup legs, fy is the yield strength, d is the effective depth, and s is the center-to-center spacing of stirrups.
What is the phi factor for shear and why is it lower than for flexure?
The strength reduction factor phi for shear is 0.75 per ACI 318, compared to 0.90 for flexure in tension-controlled sections. This lower factor reflects the brittle nature of shear failures, which provide less warning before collapse. The design shear capacity phi-Vn must exceed the factored shear demand Vu at all critical sections. The critical section for shear is typically located at a distance d from the face of the support.
How do I calculate the load-bearing capacity of a beam?
Beam capacity depends on material, cross-section dimensions, span length, and support conditions. For a simple rectangular wood beam, bending strength = (F_b x b x d^2) / 6, where F_b is allowable stress, b is width, and d is depth. Always consult a structural engineer for critical applications.
How accurate are the results from Beam Shear Capacity Calculator?
All calculations use established mathematical formulas and are performed with high-precision arithmetic. Results are accurate to the precision shown. For critical decisions in finance, medicine, or engineering, always verify results with a qualified professional.