HW8Solution - UNIVERSITY OF CALIFORNIA BERKELEY Spring 2016...

UNIVERSITY OF CALIFORNIA,
BERKELEY
Spring 201 6
Department of Civil and Environmental Engineering
Instructor: J. P. Moehle
CE 120 - Structural Engineering
Solutions of Assignment No. 8
Due: April 4 , 201 6
Problem 1 - Draw influence lines as specified below:
(a) Both reactions and the shear and moment at B.
2. Impose a unit virtual displacement at A in the direction of R
A
.
3. Draw the displaced shape in a way that point c does not move.
3. Draw the displaced shape without moving the supports.
4. Find the ordinates from similar triangles.

Page 2 UNIVERSITY OF CALIFORNIA, BERKELEY
Department of Civil Engineering
CE 120 - Instructor: J. P. Moehle - Spring 201 6
IL for M
B
: By virtual displacement method,
1. Make a cut at B.
2. Impose a unit relative rotation without any relative displacements. That is, a kink will form at B.
3. Draw the displaced shape without moving the supports.
4. Find the ordinates from geometry
δ =θ1*10= θ2*20….(i)
θ
1
+ θ
2
=1 …….(ii)
solving (i) and (ii), θ
1
= 2/3 and θ
2
=1/3
so, ordinate at B= 2/3*10=20/3.
(b) The shear and moment at A, B, and just to the left of C.

Page 3 UNIVERSITY OF CALIFORNIA, BERKELEY
Department of Civil Engineering
CE 120 - Instructor: J. P. Moehle - Spring 201