Question

Two rectangular bars, one of steel and other of brass, each 30 mm x 10 mm are placed together to form a beam 30 mm wide and 20 mm deep on two supports 0.75 m apart. The brass bar is on the top of steel bar. Determine the maximum central load if the bars are, (a) separate and can bend independently, (b) firmly secured to each other throughout their length. The maximum permissible stresses in brass and steel are 70 MPa and 105 MPa respectively. Eg 85x 103 MPa and E,- 300 x 103 MPa. 6. 15

Answer 1

Calculate the moment ration using compatibility equation. Eyl, E,I, 5 (300x10)1 85x10)I -3.53 Calculate the net moment equation = 3.53M,b + M,b - 4.53M rb Calculate the moment due to the load for brass PL P(0.75) 4.53M,) -0.1875P Mr)-41.39p Calculate the stress ratio

75 75 f, 3.53 f 3.53 Calculate the stress value f 105 MPa 105-29.75 MPa 3.53 3.53 Since, < (S),α or < 70 MPa . Therefore, limited value of load will be calculated on brass material basis 10 (41.39P) 30x10 12 29.75- 30x10 2 P- (29.75)1210)41.39 - 359.39 N

Calculate the equivalent length of brass strip. -30 E, = 30%1 300x103 85x10 -105.88 mm Consider the equivalent figure 30 mm NA 105.88 mm Calculate the position of neutral axis from base line (30x10)(15) +(105.88x20)(5) (30x10)+(105.88x20) - 6.24 mm Calculate the moment of inertia about neutral axis.

x 103 300010(010)(5-620 200 x103 = t(200x10)(10-624)2 +30x10 t(30x10)(15-624)2 704 63. 1 5 mm Calculate the maximum central load using limiting value of stress' condition. P(0.75x10 (6.24) 29.75 (70463.15) (29.75)(70463,.15) 0.75x10 (6.24)- -1791.69 N