CIVL3310 STRUCTURAL ANALYSIS

Professor CC Chang

Chapter 4: Chapter 4: Internal Loadings Developed in Structural Internal Loadings Developed in Structural

MembersMembers

Internal loadings at a cross section

xA

yA yB

P wA

B

Sign Convention +

w

-

w

+x+y

Coordinates

yA

xA

P wM

V

N

yB

wM

V

Example 4.1

Sign Convention +

w

-

w

Force, Shear and Bending Moment

+

w

M+dM

V+dV

VM

dx

wdx

dV

Vdx

dM

DCCD

DC wdxVVdV

DCCD

DC VdxMMdM

P w

A B

VC VDC D

Force, Shear and Bending Moment

V-P

V

dx

P

Shear force moves toward negative direction

+M-Mo

M

dx

Mo

Moment moves towardNegative direction

x

V

V-P

P

x

Mo

M-Mo

M

Shear Force & Bending Moment Diagram

P

A BL/2 L/2

V

+P/2

-P/2

M

+PL/4

wdx

dV

Vdx

dM

M

+PL/4

Plotted on the tensile side

Need to know deflection shape qualitatively

2

2

dx

yd

EI

M

EI

M curvature

+M-M

Shear Force & Bending Moment Diagram

Structure under loads

wdx

dV

Vdx

dM

2

2

dx

yd

EI

M

Qualitative deflection shape

Bending moment diagram

Shear force diagram

Bending moment diagram(plotted on the tensile side)

Slope of V = load

Slope of M = V

Shear & Moment Diagrams for a Beam

Sign Convention

+

w

-

w

wdx

dV

Vdx

dM

Example 4.8

PL

Moment plotted on the tensile side

Examples

© 2009 Pearson Education South Asia Pte Ltd

Structural Analysis 7th EditionChapter 4: Internal Loadings Developed in Structural Members

Example 4.8

Draw shear force and bending moment diagrams

Solution

mx

xxF

V

y

205

09

20

2

1300

0

.

kNmM

M

M s

104

03

20.520.5

9

20.520

2

1)20.5(30

0:ve- asmoment iseAnticlockw

9m

Reflection: What Have You Learnt?