Question

Influence Lines of a Three Span Beam

(A) For the structure shown below, calculate/ determine:

a. The maximum design Moments (both positive and negative)

b. The maximum design Shears

c. The maximum design Reaction at \(A\) (both positive and negative)

d. The maximum design Reaction at \(\mathrm{B}\) (both positive and negative) when a unit point load moves across the structure.

(B) If the Dead Load (DL) udl is \(w \perp L\), and the Live Load (LL) udl is \(w \perp L\), calculate/ detemine the design values for:

a. Moments (both positive and negative); these can be at various points along the structure

b. Shears: these can be at various points along the structure

c. Reaction at \(A\) (both positive and negative)

d. Reaction at \(\mathrm{B}\) (both positive and negative) Indicate the positions of where the udl's must be placed to achieve the worst effect for design. Indicate were the design moments and shears are located.

(C) State all assumptions that you have made

Answer 1

I > С C L Moment ar = xx (2-x) xxl 2L-a А A y ti (24-a) (ab > *(1-x)= x XL-XXX (XL-2X (2L-a) 2L-a (CL-BY)x (21-a) y I x1= BM: L SF (21-a) 3L SF at positive at + M 2L-a (24-a) 3L 2L-a 8L-X M-C2L-a) x (2L-a) (32-2) SF=(21-a) x (21-a) x 1 (3L-1) (3L - ®) 6 Samay ZL-a 32 æ 3L 0 SF max XI Max & Reaction at a=1 1 and minzo A D 0 B A TA Max Reaction at B =1 min at Bao .

Max Reaction at Az + C D and min = 0 A x B D 0 + X B Max Reaction at B=1 min at B = 0,

Answer 2

I > С C L Moment ar = xx (2-x) xxl 2L-a А A y ti (24-a) (ab > *(1-x)= x XL-XXX (XL-2X (2L-a) 2L-a (CL-BY)x (21-a) y I x1= BM: L SF (21-a) 3L SF at positive at + M 2L-a (24-a) 3L 2L-a 8L-X M-C2L-a) x (2L-a) (32-2) SF=(21-a) x (21-a) x 1 (3L-1) (3L - ®) 6 Samay ZL-a 32 æ 3L 0 SF max XI Max & Reaction at a=1 1 and minzo A D 0 B A TA Max Reaction at B =1 min at Bao .