Bending Moment

CHAPTER 4:
INFLUENCE LINE OF DETERMINATE BEAM AND FRAMEWORK

Objective:
1. To Sketch diagram of influence line for reactions, shear force and moment for:
a. Simply supported beam
b. Simply supported beam with one end overhanging
c. Simply supported beam with both ends overhanging.

2. To calculate shear force and moment using influence line
3. To determine maximum shear force and moment
4. Calculate Absolute Maximum Moment (MMM)

4.1 INTRODUCTIONS:

Influence line is to:
Analysis a structure due to moving load along the beam.
Show the changes in reaction, shear stress, moment and displacement in certain point in structure when applied a unit load.
Determine the greatest position the greatest value of live load in beam.

4.2 DIFFERENCES BETWEEN INFLUENCE LINE DIAGRAM (ILD) AND BMD (BENDING MOMENT DIAGRAM)

INFLUENCE LINE DIAGRAM
(ILD)
BENDING MOMENT DIAGRAM (BMD)
a) Static and Moving Load
b) Diagrams show only one point on the beam.

c) Calculations based on the virtual load.
d) Straight line only
e) Calculations do not refer to reactions of beam.
f) Unit: m
a) Static load only.
b) Diagram shows the moment at all points on the beam.
c) Calculations based on real loads.
d) Straight lines and curves.
e) Calculations based on the SFD.

f) Unit : kNm

4.3 BASIC CONCEPT TO DRAW INFLUENCE LINE DIAGRAM (ILD)

1 unit x A B C

a b

RAY = [L-x]/L 1-x/L RCY=x/L

4.3.1 REACTION

ILD RAY L/L

b/L [+] 0

ILD RCY L/L a/L

1 [+]

4.3.2 SHEAR FORCE OF BEAM

ILD Vc b/L

[+]

[-]

a/L

4.3.3 BENDING MOMENT OF BEAM

ILD Mc 0 0
[+]

ab/L
EXAMPLE 1: SIMPLY SUPPORTED BEAM
Draw Influence Line Diagram for reaction at A and B, Shear force and bending moment for the beam. 1 unit x A C B

7.5m 2.5m

RAY = [L-x]/L 10m RBY=x/L =1-x/L

EXAMPLE 2: SIMPLY SUPPORTED BEAM WITH