Which is the correct expression for the design bending strength of a laterally unsupported beam (IS 800: 2007)? fbd = design bending compressive stress, βb = Ze/Zp for semi-compact sections (1.0 for plastic and compact), Ze = elastic section modulus, Zp = plastic section modulus.
Try it first: pick an option, then read the explanation.
Asked in SSC JE 06/06/2024 (9 am–11 am)
Detailed Explanation
The book places this steel-design question in the fixed-beam chapter. A beam without lateral support can fail by lateral–torsional buckling before reaching its full moment capacity, so IS 800 replaces fy/γm0 by a reduced design bending compressive stress fbd.
\[ M_d = \beta_b\,Z_p\,f_{bd}, \qquad f_{bd} = \chi_{LT}\,\frac{f_y}{\gamma_{m0}} \]
Why “Md = βb Zp fbd” Is Correct
Moment = section modulus × stress, so the strength is Md = βb Zp fbd. For plastic and compact sections βb = 1 (Md = Zp fbd); for semi-compact sections βb Zp = Ze.
Why the Other Options Are Wrong
- A. Md = βb Zp / fbd: Dividing by a stress does not give a moment.
- B. Md = Zp / fbd: Same error — modulus ÷ stress has no meaning here.
- C. Md = βb fbd / Zp: Stress ÷ modulus is dimensionally wrong.
Key Point
Laterally unsupported beam (IS 800 8.2.2): Md = βb Zp fbd, fbd = χLT fy/γm0.
Key Concepts for Students
- χLT is the reduction factor for lateral–torsional buckling.
- Laterally supported beams use Md = βb Zp fy/γm0.
- γm0 = 1.10.
Practice more: this is question 1 in Fixed Beam MCQs – Part 1. Try the whole set and check every answer instantly.