civl3310 structural analysis professor cc chang chapter 4: internal loadings developed in structural...
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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
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
Examples
© 2009 Pearson Education South Asia Pte Ltd
Structural Analysis 7th EditionChapter 4: Internal Loadings Developed in Structural Members
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
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