Question

The beam ABC is supported at A with a guided support (fixed with roller) and hinge at B has rectangular cross section and supports concentrated loads P both ends A and C as shown in the figure. The span length from A to B is L, and the length of the overhang is 1/2. Point D is located midway between the supports at a distance d from the top face of the beam Knowing that the maximum tensile stress (principal stress) at point D is = 45 MPa. determine the magnitude of the load P. (Show your calculations with Mohr's circle) Given: L = 1.9 m, b = 65 mm, h = 250 mm, and d = 48 mm. M D. Answer: P= KN

Answer 1

Maxamun tensile stress = 45tupa L-1.9m, 6: 650 his 250mm d=48mm Saution: e From Ewllision Equations have 12 0 95 m EMA =0 0.95m 0.95m RB XL = Px 31 HAS RB

© E MB = IHA =0 b HA X) = 48mm 19 h- 250 D at point Moment M = + PX 65 PX & - Pu cobo Х 2 2 bha I y 12 Cobo 3 PL 3 PX 1900 65x2502 -1.483X10-3 p 249 the shear stress. finding x. 49 77 2 d I X AY b TD- bha 2 PX12X77 To = Costa +1.1372X10 4P **)+103 GSXQ50) Principal stress Die Betsy 1 (x=89) + (exy)? »°p)*= [[:40X10 27} 403x10 45 = 2x 2 P = 318 66.127 N

Drawing Mhor's wice, Ca, upal 3-655 AD: (19x, Exy) )حنا- nj 20p 6) the 44. 72/45 Mpa) D. Average normal strain Mhors click Fig .: (Does TH= 1.403x1093 XP La 44.708 Mapa - 1.1473810-4P ITD 3.655 mpa x