Advanced Methods of Structural Analysis

202 6 Deflections of Elastic Structures

(a)Vertical displacement of joint 4
(b)Mutual (relative) displacement of joints 2 and 3
(c)Angle of rotation of the bar 1–3
(d)Mutual angle of rotation of the bars 1–3 and 3–5

h=3m

1

d = 4m

(^35)
2 4 6
A B
+45°C
–30°C
Fig. P6.16
Ans. (a)4tD800 ̨ .m/.#/I.b/ 23 D321 ̨.m/I
.c/ 13 D80 ̨ .radian/.clockwise/I.d/ 13  35 D60 ̨ .rad/.
Problems 6.17 through 6.28 are to be solved by graph multiplication method.
6.17.Cantilevered nonuniform beam is subjected to concentrated load P
(Fig.P6.17). Calculate the verticaldisplacement of free end.
l
l l
EI 1 EI 2
P
Fig. P6.17
Ans.yD.1C
^3 /
Pl^3
3 EI 1
;
D
1
n
1; nD
I 2
I 1
6.18.A nonuniform cantilevered beam AB carrying the distributed load q
(Fig.P6.18). Bending stiffness equalsEIon the segmentCB D 0:5landkEI
on the segmentAC D 0:5l; parameterkis any positive number. Calculate the
vertical displacementAat the free end. Analyze the limiting case.
l/ 2
q
A B
kEI C EI
l
Fig. P6.18