Advanced Methods of Structural Analysis

38 2 General Theory of Influence Lines

Fixed load approach Determine the reaction of supportB; Construct the internal
force diagrams.

Moving load approach

(a)Construct the influence lines for vertical reactionRBand momentMBat the

clamped support

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

(c)Calculate reactions at the supportB, bending moment and shear for sectionk

using corresponding influence lines

(d)Compare the results obtained by both approaches

Ans.RBD14:0kN."/IMBD 57 kNm.

q=2kN/m

A B

P=8kN

3m k 3m

Fig. P2.3

2.4.The beamABis subjected to the fixed uniformly distributed loads as shown in
Fig.P2.4. All dimensions are in meters.

(a)Calculate the bending moment and shear at sectionkcaused by the given fixed

load using influence lines forMKandQK, respectively

(b)Calculate the bending moment and shear force at sectionkcaused by the given

fixed load, using influence lines forreactionRA

(c)Compare the results

Ans.MkD 9 kN m;QkD1:8kN.

3 332 2 3

ABk

q=2kN/m

Fig. P2.4

2.5.Explain the meaning of the graph, which is obtained from any influence line
by its differentiation with respect to axial coordinatex.