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CIV100 – Mechanics
Module 5: Internal Forces and Design
by: Jinyue Zhang
2010/10/26
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Module Objective
•
By the end of this Module you should be able to:
–
Find internal forces of any structural members
–
Understand how Shear Force Diagrams (SFD) and Bending Moment Diagrams
(BMD) relate to the internal forces in structures
–
Know how to draw SFD for beams
–
Know how to draw BMD for beams
–
Understand how different load types (concentrated load, distributed load, couple)
affect the shape of SFD and BMD
–
Understand the design of structural members in tension
–
Understand the design of structural members in bending
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2010/10/26
2
Today’s Objective
•
Understand the concept of internal forces
–
How to find internal forces of a structural member
•
Understand the concept of SFD and BFD
– How to draw SFD and BFD of a beam with simple loading
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Internal Forces
•
We have learnt this concept!
3
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Internal Forces
•
Now let
’
s look at multiforce member!
0
0
0
=
=
=
∑
∑
∑
Mo
Fy
Fx
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Internal Forces
•
Naming those internal forces
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6
Finding Internal Forces – Procedure for Analysis
•
Solve the whole structure first, find
all reaction forces
if necessary.
•
For frames and machines or their combinations,
dismember
the
structure and obtain the
reactions at each connection
.
•
Keep all distributed loadings, moments, and forces acting on the
member in their
exact location
, then cut the member to analysis by
an imaginary section at the point where the internal loading is to be
determined.
•
Draw FBD
of the segment that has the least number of loads and
apply EoE
to find internal forces:
–
Make assumption on unknown forces about their sense, if the EoE yields a
negative scalar, your assumption was wrong.
–
Moment should be summed
at the cutting section
where we eliminate the
unknown normal and share forces.
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Example 1
•
The bar is fixed at its end and is loaded as
shown. Determine the internal normal force at
points B and C.
5
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Example 1
•
The bar is fixed at its end and is loaded as shown. Determine the internal normal force at points B and C.
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Example 2
•
Determine the internal normal force,
shear force, and bending moment at
point B.
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10
Example 2
•
Determine the internal normal force, shear force, and bending moment at point B.
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Today’s Objective
•
What is Bending Moment Diagram (BMD)
•
What is Shear Force Diagram (SFD)
•
Understand the sign convention of BM and SF
•
2 examples of plotting SFD and BMD
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SFD and BMD
An Interesting Applet!
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Sign Convention for Bending Moments
•
In North America, if the moment tends to cause the beam to
curve upward
it is
positive
; if the moment tends to cause it to
curve downward
it is
negative
.
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This document was uploaded on 12/23/2010.
 Spring '10

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