Question

Draw the shear and moment diagram for each of the three members of the frame. Assume the frame is pin connected at A, C, and D and there is a fixed joint at B?

Answer 1

Consider portion CD, Cv Cx 15 KN/m 6 m Dx Dy Taking moment about point C, 2(6)-(15x6ร์" D. (6) 270 D, = 45kN

C, 90-45 C 45kN Taking moment about point A, D. (6-4)+D, (5)-(50x1.5)-(40x3.5)+(90x1) 0 45(6-4)+D, (5)-75-140+90 0 90+D, (5)-75-140+90-0 D, (5)-35 Considering portion BC, 40 kN 2 m 1.5m 50 kN 1.5 m C-45 kN 8 C-7KN

F0 7-50-40+ B,0 В.=-7+50+40 B. 45kN Taking moments about B, M-(50x1.5)-(40x3.5)+(7x5)=0 M 75+140-35 Consider portion AB,

83 kN 180 kN-m 45 kN 2m A-45 0 A 45kN 4-83-0 83kN Let X-X be the section between AB at a distance x from end A, Shear force calculation =-45kN Bending moment calculation

M. : 4(x) --45(x) atx=4m,M,--45x4 --180kNm Shear force and bending moment diagram of member AB, -45 45 kN -180 kN-m Considering portion BC, Let X-X be a section between BC at a distance x from end B

50 kN 40 kN ← -45 kN ↑ 1.5m, 2m ,L5 m↑ 7 kN 8.3 kN Shear force calculation: Bending moment calculation: M180+83x at x = 15,ME=-180 +(83x1.5) --55.5kN.m Let X-X be a section between EF at a distance x from end C: Shear force calculation:

33kN E-F = 33kN Bending moment calculation: M. = 7x-40(x-1.5) atx=15,M,-7x15-40(15-15) 10.5kN-m Let X-X be a section between FC at a distance x from end C: Shear force calculation: Bending moment calculation:

50 kN 1.5 m2 40 kN 2 m 1.S m 45 kN 180 kN-m 33 kN Shear force C diagranm 8 7 kN 10.5 Bending C moment diagram 55.5 -180 Consider portion CD, Let X-X be a section between CD at a distance x from end C: Shear force calculation

7-45kV-(15xx) at x = 3,V-45-45-0 at x = 6,V =-45kV Bending moment calculation: M 45(x)-15xxx- = 45x-75x2 atx- 3mM -45x3-7.5x32 = 67.5kN m at x = 6"MD=45x6-7.5 x 62 Plot the above values,

-D 6 m 45 Shear D force diagram 3 m 67.5 kNm45 kN Bending moment Ddiagram