Engineering 1
Structural
Analysis
Tom Rebold
Engineering-1: Intro to Engineering
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To design a bridge, the internal
forces must be understood
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Outline
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Force vectors
Adding vectors
Tension and Compression
Assumptions
Method of Joints
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Vectors help us understand
forces
 Have a direction
 And a size
 Applied to bridges
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Adding Vectors
 Imagine you walk N for 2 blocks,
turn and walk E for 2 blocks
turn and walk S for 2 blocks
 Where did you end up?
• That’s exactly how you add vectors
 For a bridge not to collapse, all the
forces at each joint must add to zero
• i.e. you arrive back where you started
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Tension and Compression
 Who knows the difference?
 In our diagrams, a force acting toward
the center of a member (pulling on a
pin) is tension. A force pushing a pin
outward from a member is compression
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Assumptions
 All loadings are applied to the joints
 The members are joined by smooth pins
Conclusion 1: each truss member acts as a
two force member
Conclusion 2: forces can only elongate
(tension) or shorten (compress) a member
 Also assume the weight of the members
is small compared to the load
 At each joint, the sum of all forces must
be zero (or the bridge would collapse)
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Method of Joints
 Start at a joint with one known force and at
most two unknown forces
 Draw the “free-body” diagram of a joint,
removed from it’s surroundings
 Apply the known force to the joint, then zero
out the known force by adjusting the force
vectors along the other two members
 Once you determine the force at one end of a
member, it’s the same force at the other end
 Continue to analyze each joint, where at most
you have two unknown forces to solve
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We now demonstrate on the
homework examples
1 end is
anchored to
the ground
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1 end is set
on a roller
Problem 2
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Computer Analysis Tool at
http://www.jhu.edu/virtlab/bridge/bridge.htm
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As the length increases, so do the
forces…
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Shifting the load…
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