Question

As per IS:800-2007, design of a cantilever steel beam section for its moment capacity requires fulfilment of an upper bound, expressed as:
\[ M_d \le 1.5 Z_e \frac{f_y}{\gamma_{m0}} \]
The reason for such upper bound is to

• A. control deflection
• B. restrain lateral-torsional buckling
• C. avoid plastic deformation under working load
• D. avoid yielding at ultimate load

Hint:

Compare the plastic-modulus based \(M_d\) with the first-yield moment \(Z_e f_y/\gamma_{m0}\); the 1.5 factor is a working-load serviceability safeguard, not a buckling or deflection check.

Answer 1

The Correct Option is C

This question checks why IS 800:2007 caps the design moment of a laterally supported beam at $1.5 Z_e f_y/\gamma_{m0}$ even though the main formula uses the plastic modulus $Z_p$. Look at each option as a possible purpose of that cap.

1. Control deflection: deflection is checked independently, comparing actual deflection under service loads against a span/depth limit. It has nothing to do with the $Z_e$ based moment cap.
2. Restrain lateral-torsional buckling: buckling is controlled through the reduction factor $\chi_{LT}$, applied in a separate step. The $1.5Z_e$ limit applies even to fully laterally restrained beams, where buckling is not a concern, so this cannot be the reason.
3. Avoid plastic deformation under working load: the shape factor $Z_p/Z_e$ can sit well above 1.5 for some sections. Without a cap, the design moment from $Z_p$ could sit far higher than $Z_e f_y/\gamma_{m0}$, the moment that first causes yielding at the extreme fibre. That would mean the beam starts to yield and pick up permanent curvature while carrying only its everyday working load. Capping $M_d$ at 1.5 times the first-yield moment keeps this margin under control.
4. Avoid yielding at ultimate load: limit state design accepts, and depends on, some yielding and redistribution at the ultimate load stage, so preventing all yielding there is not the design intent.

Ruling out A, B and D leaves the third statement: the bound exists so the member does not pick up excessive plastic deformation while still resisting working loads.

Let's summarize:

• $M_d=\beta_b Z_p f_y/\gamma_{m0}$ can overshoot the first-yield moment $Z_e f_y/\gamma_{m0}$ by more than 50% for high-shape-factor sections.
• The $1.5 Z_e f_y/\gamma_{m0}$ ceiling keeps that overshoot in check under working loads.

So the correct option is (C): avoid plastic deformation under working load.