Question

QI A cantilever beam carries a horizontal point load of 100 kN at its end, as shown in Figure Q1 (a). In this case, the self weight of the beam must be included. The beam is made from a square box section with a width of b and a depth of b (refer to Figure Q1 (b)). The density of the beam is 20 kN/m and the maximum allowable longitudinal stress of the beam is 200 N/mm². Figure QI (a) Figure Q1 (b) (a) Determine the reactions, and draw the corresponding shear force and bending moment diagrams. [10] (6) Calculate the cross-sectional dimension of the beam. [10] (c) Draw the combined stress distribution across the section at fixed end. [5]

Answer 1

P: 100KN Given! A cantilever beom Carries a horizontal point load of its end Ond density of beam w: 20kn/m?, we 20x10 q2 Nlm moumum allowable longitudinal stress, T 2ov N/mm² L Reaction bcom of the Assum length Rx .ps 100 KN By = 209*LKIN Shear foro diagram combined stress Ry across the distribution section at tired end. bottom side Zt (odtob) A Bending moment diagrum ed trb) G B transverse G shear stress mA = 2001/KNM 6 Cross secticocl dimension of besm (9) - mpa now asic stren P = 105 G2 az 6m bending stress of = a) 64209% (1000)? 6x102 mea oba a 2 43 o ind i tall hoo , (negleer transverse sheer stress) 105 6x107 1 200 Cross-secnim A = 30x300mm 42 2006?- 6x10*a -105=0 a = 360mm