Advanced Methods of Structural Analysis

260 7 The Force Method

7.2.A clamped-pinned beam is subjected to coupleM 0 at the roller support
B(Fig.P7.2). Find the reaction of supports and construct the bending moment
diagram.

l

M 0

A B

MA RA RB

Fig. P7.2

Ans:MAD0:5M 0 I RADRBD

3

2

M 0

l

7.3.Fixed-pinned beam is subjected to concentrated forceP at the midspan
(Fig.P7.3). Find the reaction of supports and construct the bending moment di-
agram.

l

A B

P 0.5l

C

MA

RA RB

Fig. P7.3

Ans:MAD

3

16

PlI MCD

5

32

PlI RBD

5

16

P.

7.4.The beamABwith clamped supportAand elastic supportBis subjected to uni-
formly distributed loadq; the stiffness coefficient of elastic support isk(Fig.P7.4).
The deflectionof supportB, reactionRBof this support and stiffness coefficientk
are related asDRB=k. Determine the reaction of supports. Consider two special
cases:kD/,kD 0.

A

q

B

k

l

l

Fig. P7.4

Ans:RBD

3

8

ql

1

1 C ̨

; ̨D

3 EI

kl^3