Shear and Torsion in Beams

Shear and Torsion in Beams

Shear failures in reinforced concrete are brittle and sudden, making them more dangerous than flexural failures. Therefore, design codes typically require a higher safety margin for shear.

Shear Strength

The nominal shear strength $V_n$ is the sum of the concrete contribution $V_c$ and the steel reinforcement contribution $V_s$.

$V_n = V_c + V_s$ $\phi V_n \geq V_u$

For shear, the strength reduction factor $\phi = 0.75$.

Concrete Contribution ($V_c$)

For members subject to shear and flexure only: $V_c = 0.17 \lambda \sqrt{f'_c} b_w d$

Steel Contribution ($V_s$)

Provided by stirrups (transverse reinforcement): $V_s = \frac{A_v f_{yt} d}{s}$

Where:

• $A_v$: Area of shear reinforcement within spacing $s$.
• $s$: Spacing of stirrups.
• $f_{yt}$: Yield strength of stirrups.

Torsion

Torsion occurs when a member is twisted about its longitudinal axis. Design for torsion involves calculating the threshold torsion $T_{th}$ to determine if torsion can be neglected.

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