Question

2. Given the beam in the figure, the concentrated load F is 600 lb, the distributed load w is 50 lb/in, a is 10 in., bis 15 in., and I is 20 in. The beam is made of steel with E equal to 30 X 10 psi. The beam is rectangular with dimensions h = 5 in and t = 2 in. Determine the following: a. The reactions and the shear and moment diagrams b. The maximum principle stress in the beam C. The deflection at the end of the beam where the load F is applied.

Can someone show e how to solve this please

Answer 1

Sol"> A e Re Let PA and Ro be the reaction foras acting on the beam. {Fy=0 RA+ Roof+wx (l-a) RA + R = 600 + 50% (20-10) RA+ R₂ = 1100 Taking moment about pt A 50x10x 15 + 600 × 20 = Rox 15 7500 + 12000 Re 115 13000b= RB so RA=1100-1300 = –20006 -ve sign indicals force cecting in downward direction

Now we diagram will draw shecer porn and Bending moment digran Goo 1200 Tiboo 850 600 7+1 S.F.D (-) 200 450 (1) - B.M.D -2000 lb- 3625

(6) The principh stress in the bean is due to complementary shica stress generated due to shear foru and bending force generated due to bending moment of bean. We are calculating this value at n=15 @ Pt B Manman she can stress e-Sy x Ay I b P A ý is distcome betwer cig of crea & N. A -b - A is the area narked Sy=85016 @ pt B e=850x 2.5x 2 x 1.25 20.8342 Ce 127.502 161 lunch? Bending struss M=3625 6 M x y La @n= 15 nich Pt B regletin muy sign = 3625 x 2.5-435.669 20.83

a Uang Maulay method to calculate deflection of the beam so moment eqr of the beam Mx - - 2003 1-50(x-1) +1300(1-15) Eldy - Mr dne - Eldy -- 2oon) - 50 (2-1) +1300 (21-15) dn' Integrciting this ego twice to get deflection Ely = -200x² +Cin+(2-50 (4-1-) + 1300 (N-18) 24. y=0 @ x=0 Boundary condition 4-0 Q n-15 EICO) - ( EICO) = -200 (15) + C, (15) -50(5)* 24 (=7586

so our eq" becomes Elye -200 n° +75862 -50 (2-1) I 24 + 1300 (N-153 Deflection at x = 20 3 Ely - - 200 (20)" + 7586 (20) – 50 (1) * 24 + 1300x5 Ely--108696.666 E- 30x loʻpsi In th= (2) (5)² = 20.83 nt 4. – 108696.666 =-1.73 x 10-4 inch 30x10x20.83 Deflection at end of becom is downwards - 1.73410" ench - so uc