Advanced Methods of Structural Analysis

3.5 Special Types of Trusses 63

The construction of the influence line for thrustHis presented here in tabulated
form. It is evident thatHADHBDH:

PD 1 left at jointC PD 1 right at joint C

H!

P

MCrightD 0 !HfCRB

l

2

D0; H!

P

MCleftD 0 !HfRA

l

2

D0;

HD

RBl

2f

!IL.H /D

l

2f

IL.RB/ HD

RAl

2f

!IL.H /D

l

2f

IL.RA/

The left portion of influence lineHcan be obtained from the influence line for
RBby multiplying all ordinates by factorl=2f. The maximum thrust caused by
concentrated loadPisPl=4f. This happens if the force is located at hingeC.

Inf. line H

lIL(RB)

2 f

l

Right-hand portion 2 f

+

Left-hand portion 4 lf

P= 1

H

f

RA RB

H

d

1

2

3

4 6 C

5

1

7

1

r

a

A B

8

r

5 d

IL(RB)

r

5 d

rfIL(H)

IL(RA)

r

d

− Construction of

r Inf. line U 3 – 5

d

g

m

m

a

b

c n

Inf. line U 3 – 5

−

a n

c

a

b

Fig. 3.21 The influence lines of the symmetrical three-hinged truss

Having the influence line for the thrust allows us to determine the internal force
in any member due to arbitrary load. Assume for example, that the right half of the
truss is loaded by uniformly distributed loadq. In this case,

HDq!D

1

2

l

4f

l

2

„ƒ‚...

!

qD

ql^2

16f

and RAD

1

2

1

2

l

2

qD

ql

8

:

After that, finding the internal force in any member is a matter of elementary cal-
culation. So the influence line for thrust should be regarded as a key influence line.