Power point lesson about influence lines

1. INFLUENCE
LINES
INFLUENCE LINE FOR BEAMS

2. INFLUENCE LINE
• Influence line represents the variation of either the reaction,
shear, moment, or deflection at a specific point in a member
as a concentrated force moves over the member
• The influence line can also be constructed by placing the unit
load at a variable position x on the member and then
computing the value of R,V, or M at the point as a function of
x. In this manner, the equations of the various line segments
composing the influence line can be determined and plotted.

3. SAMPLE PROBLEM
• Construct the influence
line for the vertical
reaction at A of the beam
in Fig. 6–1a.

4. SAMPLE PROBLEM
• Construct the influence
line for the shear at point
C of the beam in Fig. 6–3a

5. SAMPLE PROBLEM
• Construct the influence
line for the moment at
point C of the beam in
Fig. 6–5a.

6. SAMPLE PROBLEM
• The frame structure shown in Fig. is
used to support a hoist for transferring
loads for storage at points underneath it.
It is anticipated that the load on the
dolly is 3 kN and the beam CB has a
mass of 24 kg/m.Assume the dolly has
negligible size and can travel the entire
length of the beam.Also, assume A is a
pin and B is a roller. Determine the
maximum vertical support reactions at A
and B and the maximum moment in the
beam at D.

7. SAMPLE PROBLEM
• Solve Prob. 6–11 using
Müller-Breslau’s principle

8. SAMPLE PROBLEM
• The beam is used to support a
dead load of 500 lb/ft, a live load
of 2 k/ft, and a concentrated live
load of 8 k. Determine (a) the
maximum positive (upward)
reaction at A, (b) the maximum
positive moment at E, and (c) the
maximum positive shear just to
the right of the support at C.
Assume A and C are rollers and D
is a pin.

9. INFLUENCE
LINES
INFLUENCE LINE FOR FLOOR GIRDERS

10. INFLUENCE LINE FOR FLOOR GIRDERS

11. SAMPLE PROBLEM
• Draw the influence line
for the shear in panel
CD of the floor girder in
Fig. 6–21a

12. SAMPLE PROBLEM
• Draw the influence line for
the moment at point F for
the floor girder in Fig. 6–
22a.

13. SAMPLE PROBLEM
• A uniform live load of 1.8
kN/m and a single
concentrated live force of 4
kN are placed on the floor
beams. Determine (a) the
maximum positive shear in
panel BC of the girder and
(b) the maximum moment
in the girder at G.

14. INFLUENCE
LINES
INFLUENCE LINE FORTRUSSES

15. INFLUENCE LINE FOR TRUSSES

16. SAMPLE PROBLEM
• Draw the influence line
for the force in member
GB of the bridge truss
shown in Fig. 6–24a.

17. SAMPLE PROBLEM
• Consider a similar truss as
shown in Fig. 6–26a,
determine the largest force
that can be developed in
member BC due to a moving
force of 25 k and a moving
distributed load of 0.6 k/ft.
The loading is applied at the
top cord.