1. Tension and Compression in Trusses
Review
A truss is considered to be a solid beam full of holes. A truss and beam behave similarly under the same live load.
The point of a truss is to disperse forces as far from the neutral axis as possible in order to resist deflection.

2. Tension and Compression in Trusses
Review - Top-Loaded Truss
Has a live load acting on the top of the truss (roadway on top).
The area directly beneath the load is under compression and is called the “compression zone”.
Non-vertical members next to the compression members must be tension members. At each joint, the sum of the vertical (and horizontal) components of the member forces must be zero.
Therefore, for a top-loaded truss, non-vertical members beyond the compression zone must be in tension and compression, alternately distributed.

3. Tension and Compression in Trusses
Review - Bottom-loaded Truss
Has a live load is acting on the bottom of the truss (roadway on the bottom),
The area above the load is under tension and is called the “tension zone”.
Non-vertical members next to the tension members must be compression members.
Therefore, for a bottom-loaded truss, non-vertical members beyond the tension zone must also be in compression and tension, alternately distributed.

4. Tension and Compression in Trusses
You can mathematically analyze a truss with the “Method of Joints”
The method of joints states:
Each joint of the truss must be in equilibrium
For each joint, the net force in the x- and y-directions must equal zero.

5. Tension and Compression in Trusses
For a truss to be effective:
the sum of the forces in the x-direction must equal zero
the sum of the forces in the y-direction must equal zero
the moments of force must equal zero.
Your bridge is either top or bottom-loaded. There is no horizontal component of force, therefore ΣFx = 0
Pinned and roller joints

6. Tension and Compression in Trusses
To analyze a truss for static loads
1. Determine if the truss is statically determinate. Then you can use the static equilibrium equations to analyze the truss.
Use the equation:
2J = M + 3
where J = number of joints, and M = number of members

7. Tension and Compression in Trusses
2. External Forces
Calculate the sum of the forces in the x-direction – remember to set the sum equal to zero.
Calculate the sum of the forces in the y-direction – remember to set the sum equal to zero.

8. Tension and Compression in Trusses
3. More External Forces
Moment – a moment of force is the product of a force and its distance from an axis, which causes rotation about that axis.
Sum the moments in the y-direction to solve for the unknown. Then substitute into the external forces equation to solve for all external forces.
Start with the sum of the moments about the first joint.
If the joint would rotate clockwise when the force is applied, the moment is negative.
If the joint would rotate counterclockwise when the force is applied, the moment is positive.

9. Tension and Compression in Trusses
4. Internal Forces
Start with the pinned joint where you know two external forces. Do not use moments when calculating internal forces – only external forces.
Draw a free-body diagram at that joint.
Always measure angles with respect to the positive x-axis.
Solve for the forces acting on each member in the truss.
Members in compression have negative internal forces.
Members in tension have positive internal forces.
Pinned and roller joints

10. Tension and Compression in Trusses – Analyzing your bridge
We will say that your bridge is vertically loaded with 100 N (about lbs) of force downward (-100 N). That means that the sum of the forces in the vertical direction must equal 100 N.
ΣFy = 100, therefore Fy(joint1) +Fy(final joint) = 100
Start with the sum of the moments about the first joint.
ΣM(joint 1) = (100 N x the distance the force is from the joint, in meters) + (Fy on the opposing joint x distance from joint) = 0