Advanced Methods of Structural Analysis

24 2 General Theory of Influence Lines

Fig. 2.6 Beam with

overhangs. Construction of

influence lines for bending

moment and shear at

sectionk

P= 1

l

k

ab

Inf. line Qk

Inf. line Mk

l

ab

+

+

1

1

−

Inf. line Mk (m)

a

l b

ab

+

P=1-variable position

RA l RB

k

ab

AB

Bending moment

diagram M (kNm)

P-fixed position

l RB

ab

B

l

Pab

k

Load contour Extended fibers

Fig. 2.7 Influence line for bending moment at sectionkand bending moment diagram due to load

P, which is located at pointk

Now let us consider a simply supported beam with overhangs (Fig.2.6). Assume

that sectionkis located between supports. In order to construct influence line for

bending moment and shear at sectionk, it is necessary to:

1.Ignore overhang and construct corresponding influence line for simply supported
beam
2.Extent of the latter until its intersection with the vertical passing through the end
of overhang

2.1.2.3 Discussion

At this point, emphasis must once againbe placed on differentiating between in-

fluence line for bending moment at pointkand bending moment diagram due to

loadP, which is located at pointk(Fig.2.7). This diagram is constructed on the

tensile fibers.

Even though both diagrams look similar and have same sign (ordinates of bend-

ing moment diagram are positive) and same ordinate at sectionk(ifPD 1 ), they

have completely different meanings and should not be confused. The difference be-

tween them is presented in Table2.1