Advanced Methods of Structural Analysis

366 10 Influence Lines Method

10.5.Analyze each design diagram in Fig.P10.5and choose the most effec-
tive method for analytical construction of influence line for bending moment at
sectionk.

k

a

k

b

k

c

k

d

Fig. P10.5

10.6.Design diagram of a uniform semicircular two-hinged arch subjected to trav-
eling loadP D 1 is presented in Fig.P10.6. Flexural stiffness of the arch isEI,
axial stiffness of the tie isEtAt. Derive expression for trussHin terms of the angle
'. Take into account displacement of thearch due to bending deformation of the
arch itself and axial deformation of the tie. Analyze limiting case (EtAtD 0 ,and
EtAtD1).

P=1

x

y

R

l=2R

O

j Tie

EI=const

Et At

A B

Fig. P10.6

Ans.HD

1

C 4

E

Et

I

AtR^2

f.'P/; f .'P/D 2



3

4

cos^2 'PC

1

4

cos2'P



z

10.7.Uniform two-span beams with equal spans are presented in Fig.P10.7;the
flexural stiffnessEIis constant. Construct the influence line for angle of rotation at
the middle support. Construct the bending moment diagram, if forcePD 100 kN
is located at point 8; use the influence line for primary unknown.