Question

The beam shown in the figure consists of a W360 79 structural steel wide-flange shape [E = 200 GPa; 1 = 225 x 100 mm"]. For the loading shown, determine: (a) the reactions at A, B, and C. Enter a positive value for a reaction force that acts upward on the beam, or a negative value for a reaction force that acts downward. (b) the magnitude of the maximum bending stress in the beam. Enter a positive value for the magnitude. Note: Use the tabulated value for the section modulus S from Appendix B directly in the stress calculation. Although S is related to the area moment of inertia I and the cross-section depth d, due to round-off in the tabulated data for S, I, and d, a slightly different answer for the bending stress is obtained using S directly as compared to the result obtained in using I and d. Of course, performing the calculation using either S directly, or using I and d, the answer will likely be within the required tolerance. Assume L1 = 3.0 m, L2 = 5.7 m, M = 164 kN · m, and w = 93 kN/m. W го в (a) Ay = (b) Omax =

Answer 1

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Solution Criven Dater - 2 = 3m, 4- 5.7m, M = 164 KN W = 93 KN/m F= 200 bifa, I = 225x10 mm W360x79 Structural stell Consider down ward deflection of simply Supported beam at B due to UDL. Ve= - Wa² (42²_791 +392) QULEI VB = - 93% (517)3 (4x (8.7) ² 4x57887 24 x 8.7XEI + 3x (5.7) 2) - 4379.979 N-m3 - Consider the down word deflection of simply supported beam at B dul to concentric Moment: -

M MX (21 2 - 32x+x2) GLEI - - 16483 (2218.7) ² _ 3x8,783 +(372) 6X817X EI Ve = -773•628 XN-m3 EI Conndur the upward deflection of simply supporteer Boom at B dul to concentrated load Rye Vo = - Pab (2²q²_82) GLEI putting, P = - RB, L = 8,7m, a=3m 6=517m Vo = + RB X 38517 (1817) _ (3) ² (57) ? 688178 EI Vo = 1.203 Re] 111203 RB EI

Compatibility equation for deflection af B - 4379.974 EE 773.628 4 11.203 K2_0 EI EI RB = 460 • 02 KN (1) Rox 3 + RX817 - 1648 - 9385:78507 460.0283 + RX8 17 - 164 -3021057 = 0 The = 207.53 KN GA E fy=0 Ret Ret Re - 9 3x5:7=0 RA +460.02 + 207.53-53001=0 RA= -137.45 TRA= 137.4567

63 mm (bo) Mugnitude of Maximum Bending stellt Section phroperties from Appendix B) I= 2253106 m) 5= 1270 x 103 mm - Bending stress at maximum Moment Jos 164 X 353/2 71100012 225x106 V = 1281649 MPa