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How to Calculate Loads on Wooden Trusses

Updated April 17, 2017

The wooden truss is one of the most important structures in modern engineering. Proof of the truss's versatility and strength comes in the form of bridges, high-rise buildings and residential roofing. Trusses consist of members, the lengths of wood that make up the structure and joints or "nodes," the fittings that connect the members together. Truss loads exert all of their force on the joints by way of the members. By carefully following the process of how to calculate the load capacity of a wooden truss, you can compute the maximum load capacity that a truss can handle before building the structure.

Test the stability of the truss. A statically sound truss follows the equation:

2 X j < m+3

Where" j" = the number of joints and "m" = the number of members

(2 times the number of joints is less than the number of members plus 3)

Choose a load to apply to the truss. This gives a reference to use for calculating the truss's strength.

Compute the load distribution with the equation:

Load per joint = Total load/ total number of joints

Draw one triangle of the truss on a piece of paper. Measure the lengths of the sides and hypotenuse of the actual triangle. Label the corresponding measurements on the drawing.

Draw "x" and "y" axes on the paper and decide on the positive and negative vertical directions for the axes. Likewise, decide on a positive and negative horizontal direction. This will determine if the force is applied in a positive or negative direction.

Choose one angle of the triangle and calculate the sine and cosine of the angle with the equations:

Sine of angle = length of leg opposite the angle/length of hypotenuse

Cosine of angle = length of leg adjacent to the angle/length of hypotenuse

Compute the opposing force exerted by the hypotenuse of the triangle with the equation:

Load on joint/sine of angle

Compute the force exerted by the vertical member of the triangle with the equation:

Force on hypotenuse X sine of angle

Compute the force exerted by the horizontal member of the triangle with the equation:

Force on hypotenuse X cosine of angle

Repeat all of the steps for the remaining triangles of the truss. Create a table of the forces exerted on each joint. Negative forces signify compression and positive forces signify tension.

Record the tensile and compressive strengths of each member from "length versus strength" graphs for the wood that makes up the truss.

Calculate the factor of safety for each member with the equation:

Tensile or compressive strength of member (depending on whether the member is in tension or compression)/calculated force of the member.

Add each member's factor of safety to the strength charts.

Redo the entire process for larger and larger loads until the factor of safety becomes less than two -- at that point the truss will not be able to hold the required load.

Tip

Make sure to keep to the chosen positive and negative signs; if you choose the downward force to be negative all upward forces will remain positive.

Warning

Always follow all construction codes and safety regulations when dealing with any type of truss.

Things You'll Need

  • Tape measure
  • Paper and pencil
  • Scientific calculator
  • Tensile and compressive strength tables
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About the Author

Josh Turner started writing in 2001. He wrote ad campaigns and business materials for Carpetland U.S.A. and his work has also appeared in his campus newspaper, “The Correspondent,” and “The Wellhouse” magazine. Turner is pursuing a Bachelor of Arts in mathematics with a minor in journalism from Indiana University.