Advanced Methods of Structural Analysis

Problems 201

6.14.A circular bar with central angle 80 ıis clamped at pointAand free at point
B. The bar is subjected to horizontal forcePat the free endB(Fig.P6.14). The
areaAof cross section of the bar and moment of inertiaIare constant. Calculate
the horizontal displacementBat pointB. All the three terms of Maxwell–Mohr’s
integral should be used. Estimate each termfor the following data: cross section
is rectangular.hD2b/,h=RD0:1, the shear modulusGDE=2.1C/,the
Poisson’s coefficientD0:25and coefficient D1:2.

P R x

R

y

B DB A

O

Fig. P6.14

Ans.BD

PR^3

EI

2

C

PR

EA

2

C

PR

GA

2

.

6.15.Find the horizontal and angular displacement at supportCof the frame shown
in Fig.P6.15, when the indoor temperature rises by 10 ıC and outdoor temperature
rises by 30 ıCand 20 ıC for elementsABandBC, respectively. The height and tem-
perature coefficients of the elementsBCandABareb 1 ,’ 1 andb 2 ,’ 2 , respectively.

l

h

A

B +20° C

+30° +10°

b 1 α (^1)
b 2 α (^2)
Fig. P6.15
Ans.CtD5 ̨ 1 l

h
b 1
C 3

C10 ̨ 2
h^2
b 2

1 C 2
b 2
l

.!/;
CD5 ̨ 1
l
b 1
C20 ̨ 2
h
l
.clockwise/.
6.16.Design diagram of the truss is shown in Fig.P6.16. Temperature of the top
chord of the truss decreases by 30 ıC, and of the bottom chord increases byC 45 ıC;
the temperature of diagonals and vertical elements remain constant. The coefficient
of thermal expansion of material is ̨. Compute the