Truss Concept Map - E M A 201 by Brennan Ellis

How to Evaluate a Truss

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Method of Joints

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This method evaluates each joint in a truss as a rigid particle

1) Free Body Diagram of Whole Body

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As with other evaluations, begin by drawing a FBD of the whole truss.

Sometimes it may be useful to evaluate the truss as a whole in order to find forces acting on the whole body.

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2) Free Body Diagram of Each Joint

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Each joint will be treated as a particle in equilibrium. Two equilibrium equations should be written for each joint.

3) Evaluate Each Joint Individually

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Using the FBDs drawn in Step 2, you can evaluate the forces along the x and y directions at each joint in order to solve for the reactions at each joint.

Particle Equilibrium

bjellis2 — 2021-03-11 17:58:18 UTC

Each joint can be evaluated using the idea of particle equilibrium. This is the state in which all particles in the body are not moving or translating. Two unknowns can be solved for with sum of forces equations in the x and y directions.

Method of Sections

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Can be much more efficient than evaluating individual joints in complicated problems

1) Draw Free Body Diagram

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Find the Desired Support Reactions.

2) Making a Cut

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Divide body with one or more cuts in order to isolate desired support reactions.

What to Keep in Mind

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Cuts should be made through the members you desire to find.

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Two or more cuts can be made as long as there are never more than three unknowns.

3) Evaluate Each Section

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Use equilibrium equations to evaluate each section as whole. This will allow you to solve for the desired members.

Rigid Body Equilibrium

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This considers the body as a whole. Using three equations (sum of forces in the x and y directions; sum of moments), up to 3 unknowns can be solved for.

Consider Support Reactions

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One of the first steps in the problem should be finding support reactions, which occur at points were the truss is restrained. Any direction where motion is restricted at a point will produce a reaction in that direction. These should be included in FBDs.

Making Sense of Results

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As a convention, most forces should have been drawn in tension on the free body diagram. If a negative force is the result of the equilibrium solutions, then this means that force is actually acting in compression.

Consider Zero-Force Members

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Some members can be determined to have zero force before formal analysis. This occurs in two cases: 1) In a "T" intersection, the force that is not aligned will have no force. 2) Two non-aligned members will have no force when they are the only forces at a point.

Loading Conditions at Joints

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- 4 members, aligned in pairs: the aligned members have equal and opposite forces
- 2 members aligned with a 3rd member aligned with a force P, the aligned members will have equal and opposite forces and the 3rd member carries a force equal and opposite to P
- 2 members aligned with a 3rd by itself, the nonaligned member will carry no force while the aligned members will have equal and opposite forces
- 2 aligned members carry equal and opposite forces
- 2 members not aligned with each other and with no forces present will carry no force

Static Determinacy

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The number of unknowns can be determined by the "number of members" + "number of reactions". The number of equations will be 2 x ("Number of Joints").
- If "Number of Unknowns" < "Number of Equations" then we have partial fixity.
- If "Number of Unknowns" = "Number of Equations" then we are statically determinate if fully fixed.
- If "Number of Unknowns" > "Number of Equations" then are statically indeterminate.