Question

Q1 A cantilever beam carries a horizontal point load P 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/m² and the maximum allowable longitudinal stress of the beam is 200 N/mm2.K b P= 100 kN 20 m Figure Q1 (a) Figure Q1 (b) اله (a) Determine the reactions, and draw the corresponding shear force and bending moment diagrams. [10] (b) Calculate the cross-sectional dimension b of the beam. [10] (C) Draw the combined stress distribution across the section at fixed end. [5]

Answer 1

Clue УР lookN HA zom Tom Since Thore is No Downwood force, so Roaction ganacted ad fixed and A to Resist force due to selt weight. we know, Woight & y Unit weight & Volume. of beam 20kn (62XL) MB >X find out 6 Longitudual Stross = Load Cross-sectional Area 200 N/mm2 100x103 B? B= 22.36mm

We weight of boom 20x(22.36)* x 20x103 109 200N 12000 Тел { fo HA= lookN Fr-o RA=0.2kw 0.26 0. LION + S.r.o Since Load beam so due to 100KN Act At the Coneral Axis of No bonding momont 100kN load. 6 = 22.36 SMA = 0 Pxb - Ma todox 10 2 KNM = 2lenom 10 + Olwm B.MD

Condinod stroge Fixed support. divid trass RA A 0.2 (2234)2 O. 4 N/mm² Brushing stress = z 2x10C d3 6 F41017 N/mm? Р. 1017.4 Alum? 0.4 LIN/mm2 alma = 10 INIMAL 1016.6