Advanced Methods of Structural Analysis

262 7 The Force Method

Ans.

.7:7/ RAD

P

2



3 ^2



;MCD

Plu^2 

2

.3u/; MAD

Pl

2





1 ^2



:

.7:8/ RBD

Pu^2

2

.3u/

1

1 C ̨

; ̨D

3 EI

kl^3

:

7.9–7.10.The uniform beam is subjected to uniformly distributed loadqFigs.P7.9
andP7.10). Calculate the reaction of supports and construct the internal force di-
agrams. Show the elastic curve. For problem (7.10) use the following relationship
RDk,wherekis a stiffness coefficient of elastic support andRandare eaction
and deflection of supportB.

q

l

B

A

Fig. P7.9

k

q

l

B

A

Fig. P7.10

Ans:.7:9/ RAD

5

8

qlI MAD

ql^2

8

I .7:10/ RB D

3

8

ql

1

1 C ̨

; ̨D

3 EI

kl^3

:

7.11.Continuous beam with clamped left support and cantilever at the right is pre-
sented in Fig.P7.11. Compute the bending moments at the supports 1 and 2.

1

q^ =^ 2kN/m

(^23)
P =12kN
a = ul = 6m b= ul =4mc = 2m
l 1 = 8m l 2 = 10m
F =1kN
EI = const n
Fig. P7.11
Ans.M 1 D8:013kN m;M 2 D15:975kN m