Question

A steel beam of rectangular cross section is 50mm wide and 80mm high. Please give the answer of these two questions.

ECH0013 Mechanics of Solids & Structures Exercise Sheet 5: PLASTIC COLLAPSE A steel beam of rectangular cross section is 50 mm wide and 80 mm high. The yield stress is ơr MPa. Find the percentage of the cross-sectional area is occupied by the elastic core, if the beam is subjected to a bending moment of 13 kNm acting about the horizontal axis I. : 210 [Ans. 82.5%) 2. In Q.1, find the magnitude of the bending moment that would cause 50% of cross section to yield. [Ans. M 15.4 kNm)

Answer 1

b5o mm b 80mm 8endina moment, M13 kN. m 13xio N-mm S o mm) (80mm) 1200 0 0 N-mm Plastic moment, Mp bb2 (210 NJ(So mm) (8o mm)2 2 nm 4 F63 ooooo N-mm - 16.8 kN-m - M is bejwecnMy and NM Se of the elasc core is given by (80 mm) |-/3-13 1.2.

32-95 mmm 32.9 s mnm So, percent °є cross. sectional area oc cupied by the

82.315 % C2-5 /a - Percentage o tage cross- secti on al area culpied by the 82. s 0 SiTe of elashic core - e We have e. iVen

4 2 (20mm) = ( ) 80 mm 2. 1-2 4- 3 01 89, magnitude the bending moment, M=L5yKN-m