The shape factor for a rectangular beam of width 'b' and depth 'd' is:

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OSSC JE Civil Mains (Re-Exam) Official Paper: (Held On: 3rd Sept 2023)
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  1. 1.5
  2. 2.0
  3. 2.5
  4. 3.0

Answer (Detailed Solution Below)

Option 1 : 1.5
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Detailed Solution

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Concept:

The ratio of plastic moment and yield moment is called shape factor.

Shape factor = plastic moment/yield moment

Calculation:

Shape factor (S.F.) = plastic moment (Mp)/yield moment (My)

\(S.F. = \frac{{{M_p}}}{{{M_y}}} = \frac{{{f_y}.{Z_p}}}{{{f_y}.Z}} = \frac{{{Z_p}}}{Z}\)

where, Zp = Plstic section mdulus = \(\frac{A}{2}(\overline {{y_1}} + \overline {{y_2}} )\)

Z = Elastic section modulus

F1 Abhayraj Shraddha 16.12.2020 D8

\(S.F. = \frac{{{Z_p}}}{Z} = \frac{{\frac{A}{2}(\overline {{y_1}} + \overline {{y_2}} )}}{{b{d^2}/6}} = \frac{{bd/2(d/4 + d/4)}}{{b{d^2}/6}} = \frac{{b{d^2}/4}}{{b{d^2}/6}} = 1.5\)

Important Points

Shape factor represents the reserve strength of the beam section beyond yielding. more shape factor implies more reserve strength beyond yielding moment to reach the plastic state.

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