Advanced Methods of Structural Analysis

Problems 261

A BC

ll

Fig. P7.5

7.5.Calculate the reaction and bending moment at the supportB(Fig.P7.5), if the
vertical settlement of this support.

Ans:RBD

6 EI

l^3

I MBDRAlD

3 EI

l^2



7.6.Pinned–pinned–pinned uniform beam is subjected to distributed load q
(Fig.P7.6). Construct the bending moment diagram. Consider three versions of
primary system. Primary unknown is: (1) ReactionR 1 ; (2) ReactionR 2 ; (3) Bendig
moment at support 1. Calculate the deflection at the middle of the first span.

q

ll

0 1 2

k

Fig. P7.6

Ans:M 1 D

ql^2

16

;ykD

7

768

ql^4

EI

For next problems the Canonical equations of the force method should be used

7.7–7.8.The uniform beam is subjected to concentrated forceP(Figs.P7.7and
P7.8). Calculate the reaction of supports and construct the internal force diagrams.
Show the elastic curve of the beam.

B

ul

A

ul

P

C

Fig. P7.7

ul

B

ul

A

P

C

k

Fig. P7.8