The value of nominal shear stress for beam of varying depth is given by _________.

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SSC JE Civil 05 Jun 2024 Shift 1 Official Paper - 1

\(\frac{\mathrm{V}_{\mathrm{u} \mp \frac{\mathrm{M}_{\mathrm{u}}}{\mathrm{d}}} \tan \beta}{\mathrm{b}}\)
\(\frac{V_{u \mp} \frac{d}{M_u} \tan \beta}{b d}\)
\(\frac{V_u \mp \frac{d}{M_u} \tan \beta}{b}\)
\(\frac{V_u \mp \frac{M_u}{d} \tan \beta}{b d}\)

Answer 1

Concept:

Nominal shear stress, \(\tau_v = {V_u\over bd}\)

VU = ultimate shear force at the critical section for simply supported beams.

For simply supported beams, the Critical section is at a distance “d” from support.

But in case of haunched (Varying depth) beam,

\(\tau_v = {V _{uc}\pm{M_{uc}\over d_c}Tan \beta\over bd_c}\)

Note:

‘-’ If the bending moment increase in the direction of increasing depth.

‘+’ If the bending moment increases in the direction of decreasing depth.