Trusses are structures made of interconnected triangles that are commonly used in engineering and architecture to support roofs, bridges, and other structures. The design of a truss involves calculating the forces and stresses that will act on the individual members of the truss, and ensuring that each member is strong enough to withstand those forces. Here are the general steps involved in calculating trusses:

- Determine the loads: The first step is to determine the type and magnitude of the loads that the truss will need to support. These may include dead loads (the weight of the structure itself), live loads (the weight of people, furniture, and other temporary items), wind loads, snow loads, and seismic loads. The loads are usually specified in the local building codes or engineering standards.
- Determine the reactions: Once the loads are determined, the next step is to calculate the reactions at the supports of the truss. These reactions are the forces that the supports exert on the truss, and they can be calculated using statics equations.
- Draw the truss: Draw a diagram of the truss, including all the members and joints. Label each member with its length and orientation.
- Calculate the forces: Use the method of joints or the method of sections to calculate the forces acting on each member of the truss. These methods involve applying the equations of statics to each joint or section of the truss to determine the forces acting on each member.
- Check the strength: Once the forces acting on each member are calculated, check if each member is strong enough to withstand those forces. This can be done by comparing the forces to the maximum allowable stresses for the material used in the truss. If a member is not strong enough, it may need to be replaced with a stronger member or reinforced with additional material.
- Add connections: Once the strength of each member is verified, design the connections between the members to ensure that they can transfer the forces safely and efficiently. Connections may include bolts, welds, or other fasteners.
- Check stability: Finally, check the stability of the entire truss to make sure it will not tip over or collapse. This may involve verifying that the center of gravity of the structure is within the base of support, and that the truss is properly braced to resist lateral forces.

Example 1: Warren Truss A Warren truss is a common type of truss used in bridge construction. It consists of equilateral triangles and is often used for spans between 30 and 100 feet. Suppose we need to design a Warren truss for a bridge with a span of 50 feet, a dead load of 100 pounds per linear foot, and a live load of 80 pounds per linear foot. We will use steel angles for the members, which have a yield strength of 36,000 pounds per square inch (psi).

- Determine the loads: The total load on the bridge is (100 + 80) pounds per linear foot, or 180 pounds per linear foot.
- Determine the reactions: The reactions at each end of the bridge will be half the total load times the span, or (180/2) x 50 = 4,500 pounds.
- Draw the truss: Draw a diagram of the truss, including all the members and joints. The diagram will consist of equilateral triangles connected at the vertices, with vertical members at each end.
- Calculate the forces: Use the method of joints to calculate the forces in each member. Start at one end of the truss and work your way to the other end. For example, the force in the vertical member at the left end will be 4,500 pounds.
- Check the strength: Check the maximum stress in each member by dividing the force by the cross-sectional area of the member. If the maximum stress is less than the yield strength of the steel angles, the member is safe. If not, the member must be replaced with a stronger member or reinforced with additional material.
- Add connections: Design the connections between the members to ensure that they can transfer the forces safely and efficiently. Welds or bolts can be used.
- Check stability: Verify that the truss is stable and can resist lateral forces. Diagonal bracing can be added to prevent buckling.

Example 2: Roof Truss A roof truss is a common type of truss used in residential and commercial construction. It consists of a top chord, a bottom chord, and diagonal members. Suppose we need to design a roof truss for a house with a span of 30 feet and a pitch of 6:12. The roof will be covered with asphalt shingles, which weigh 2.5 pounds per square foot. We will use 2x4 lumber for the top and bottom chords, and 2x6 lumber for the diagonal members.

- Determine the loads: The dead load of the roof will be the weight of the shingles, which is 2.5 pounds per square foot times the area of the roof. The live load of the roof will be 20 pounds per square foot, which is the minimum required by the building code.
- Determine the reactions: The reactions at each end of the truss will be half the total load times the span, or ((2.5 + 20) x 30)/2 = 330 pounds.
- Draw the truss: Draw a diagram of the truss, including all the members and joints. The diagram will consist of a top chord, a bottom chord, and diagonal members connecting them.
- Calculate the forces: Use the method of sections to calculate the forces in each member. For example, to calculate the force in the top chord at the midpoint of the span, draw a section through the truss and apply the equations of statics to the portion of the truss on one side of the section.
- Check the strength: Check the maximum stress in each