Advanced Methods of Structural Analysis

4.4 Nil Point Method for Construction of Influence Lines 95

Location of NP.Mk/may be computed by formula

uMD

lf xk

ykl 2 Cxkf

:

4.4.2 Shear Force...................................................

Step 1.Find nil point (NP) of influence lineQk.IfloadPis located on the left half
of the arch, then reaction of the supportBpass through crownC. Shear
force at sectionkequals zero, if reaction of supportAwill be parallel to
tangent at pointk. Therefore, NP.Qk/is point of intersection of lineBC
and line which is parallel to tangent at pointk. For given design diagram
and specified sectionkthe nil point./is fictitious one (Fig.4.12a).

Inf. line Qk

cosjk

−

+

*

RHP-1

RHP-2

LHP

uQ

A

C

B

1

3 5

2

k

7

6

P= 1

NP(Qk)

Tangent at k

Parallel to

tangent at k

φk b

RA RB

a

Inf. line Qk

cosjk

RHP-2

uQ

P= 1

NP(Qk)

A jk

C

B

RHP-1

−

+

*

Tangent at k

Parallel to

tangent at k

LHP

b

b

Fig. 4.12 (a)Construction of influence lineQkusing nil point method. The case of fictitious nil
point.(b)Nonsymmetrical three-hinged arch. Construction of influence lineQkusing nil point
method. The case of real nil point