Advanced Methods of Structural Analysis

Problems 37

Problems

2.1.The simply supported beamABis subjected to the fixed loads as shown in
Fig.P2.1. Analyze the structure using the fixed and moving load approach.

Fixed load approach Determine the reaction at the supports and construct the in-
ternal force diagrams, caused by given loads.

Moving load approach

(a)Construct the influence lines for reaction at the supportsAandB

(b)Construct the influence lines for bending moment and shear force for sectionk

(c)Construct the influence lines for bending moment and shear force for sections

infinitely close to the left and right the supportB

(d)Calculate reaction of the supports, bending moment and shear force for all

above mentioned sections using corresponding influence lines

(e)Compare the results obtained by both approaches

Ans.RAD3:9kNIRBD14:1kNIMkD23:4kN mIQleftk D3:9kNI

QkrightD8:1kN.

a=6m b=4m

P=12 kN q=2kN/m^

3m

k

A B

Fig. P2.1

2.2.Simply supported beam is subjected to linearly varying load shown in Fig.P2.2.
Determine the reactions of supports and construct the bending moment and shear
diagrams. Compute the reaction of the left support using influence line.

Ans.RAD

ql

6

IRBD

ql

3

IMmaxD

p

3

27

ql^2.

q

A B

l

Fig. P2.2

2.3.Cantilever beamABis subjected to the fixed loads as shown in Fig.P2.3.
Analyze the structure using the fixed and moving load approach.