Question
Download Solution PDFThe shape factor for a rectangular beam of width 'b' and depth 'd' is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
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
\(S.F. = \frac{{{Z_p}}}{Z} = \frac{{\frac{A}{2}(\overline {{y_1}} + \overline {{y_2}} )}}{{b{d^2}/6}} = \frac{{bd/2(d/4 + d/4)}}{{b{d^2}/6}} = \frac{{b{d^2}/4}}{{b{d^2}/6}} = 1.5\)
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.
Last updated on Jun 4, 2025
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