Advanced Methods of Structural Analysis

2.1 Analytical Method for Construction of Influence Lines 25

Ta b l e 2. 1 Comparison of influence line for bending moment and bending moment diagram
Influence lineMk Bending moment diagramM
This graph shows variations of bending moment
at the sectionk only;loadPD 1 ismoving
and hasdifferentlocations along the beam

This graph shows distribution of bending

moment inallsections of the beam; load

Pisfixedand acts at sectionkonly

The following example generalizes allcases considered above for construction
of influence lines of internal forces for different sections in case of simply supported
beam with overhangs (Fig.2.8).

d

Inf. line

− M 4

Inf. line

c M 3

−

c 2

Inf. line

M 2

−

Inf. line

d M^5

5

−

P= 1

243 15

cbda

c 2 d 5

Inf. line

M 1

a b

+

−

l

ab

1

Inf. line

− Q 2

Inf. line

Q 3 right

1

1

+

−

Inf. line

− (^1) Q 3 left
Inf. line
Q 4 right
(^1) +
Inf. line
Q 5
(^1) +
Inf. line
1 Q 1
(^1) +
−
P= 1
241 5
'
3'3" 4"
Inf. line
Q 4 left
1
1
−
Fig. 2.8 Beam with overhangs. Influence lines for bending moments and shear forces for different
sections
Bending MomentM 1 and Shear ForceQ 1
The influence line of bending moment at the section 1 for simply supported
beam without overhangs presents a triangle with maximum ordinateab=l,where
lDaCb. The influence line is extended within the overhang. If loadPis located
within the span, then bending moment in section 1 is positive, i.e., the extended
fibers are located below the longitudinal axis. If loadPis located outside of the
span, then bending moment in section 1 is negative.