Advanced Methods of Structural Analysis

7.3 Analysis of Statically Indeterminate Structures 223

P

ll

a=0.4l

0 1 2

n

P

02 X^1

b=0.6l

EI =constant

a

b

X 1 =1

M 1

M^0 P

(^1) P
l
Pab= 0.24Pl
c
d
e
f
l
P
l
0.4l
M (^12)
n
R 2 = 0.304P
MP
0.096Pl
0.1824Pl
P
021
n
0.096P
0.696P
0.304P
Q kN
R 0 R 1 R 2

• −
  g
  Fig. 7.8(a,b) Design diagram of a beam and primary system. (c,d) Bending moment diagrams
  in the primary system due to unit primary unknown (MN 1 /and given load (MP^0 /.(e) Primary system
  loaded by primary unknown and given load; (f) Final bending moment diagram. (g) Shear force
  diagram and reactions of supports
  Primary unknown (bending moment at support 1) isX 1 D1P=ı 11 D0:096P l.
  Construction of bending moment diagramThe bending moment diagram can be
  constructed considering each simply supported beam separately under action of
  applied load and obtained bending moments at supports, as shown in Fig.7.8e;
  constraints at the support 1 are shown apart for convenient. Final bending moment
  diagram is shown in Fig.7.8f.
  Computation of shear Having the bending moment diagram we can calculate a
  shear using differential relationshipsQDdM=dx. In our case we get