Trusses Lecture 7 Truss: is a structure composed of slender members (two-force members) joined together at their end points to support stationary or moving load. Each member of a truss is usually of uniform cross section along its length. Calculation are usually based on following assumption: The loads and reactions act only at the joint. Weight of the individual members can be neglected. Members are either under tension or compression. Joints: are usually formed by bolting or welding the members to a common plate, called a gusset plate, or simply passing a large bolt through each member. Joints are modeled by smooth pin connections.

To find the reaction forces To find the force in each member Analysis of Trusses Lecture 7 Truss Analysis External equilibrium Internal equilibrium To find the reaction forces To find the force in each member Method of joints Method of sections External Equilibrium: to find the reaction forces, follow the below steps: Draw the FBD for the entire truss system. Determine the reactions. Using the equations of (2 D) which states:

Analysis of Trusses Lecture 7 Method of Joints: to find the forces in any member, choose a joint, to which that member is connected, and follow the below steps: Draw the FBD for the entire truss system. Determine the reactions. Using the equations of (2 D) which states: Choose the joint, and draw FBD of a joint with at least one known force and at most two unknown forces. Using the equation of (2 D) which states: The internal forces are determined. Choose another joint.

Analysis of Trusses Lecture 7 Method of section (Internal equilibrium): to find the forces in any member, choose a section, to which that member is appeared as an internal force, and follow the below steps: Draw the FBD for the entire truss system. Determine the reactions. Using the equations of (2 D) which states: Choose the section, and draw FBD of that section, shows how the forces replace the sectioned members. Using the equation of (2 D) which states: The internal forces are determined. Choose another section or joint.

Analysis of Trusses Analysis of trusses (Zero-force members): Lecture 7 Analysis of trusses (Zero-force members): Analysis of trusses system is simplified if one can identify those members that support no loads. We call these zero-force members. Examples to follow: If two members form a truss joint and there is no external load or support reaction at that joint then those members are zero-force members. Joints D and A in the following figure are the joints with no external load or support reaction, so: FAF = FAB = FDE = FDC = 0.

Analysis of Trusses Analysis of trusses (Zero-force members): Lecture 7 Analysis of trusses (Zero-force members): Examples to follow: If three members form a truss joint and there is no external load or support reaction at that joint and two of those members are collinear then the third member is a zero-force member. In the following figure, AC and AD are zero-force members, because Joints D and A in the following figure are the joints with three members, there is no external load or support reaction, so: FCA = FDA = 0

EXAMPLES of Trusses: Lecture 7 Example 1: Determine the support reactions in the joints of the following truss. Calculate the force in member (BA & BC.) Solution 1. Draw FBD of entire truss and solve for support reactions: 2. Draw FBD of a joint with at least one known force and at most two unknown forces. We choose joint B. Assume BC is in compression.

EXAMPLES of Trusses: Lecture 7 Example 2: In the following Bowstring Truss, find the force in member (CF). Solution draw the FBD and find the support reactions which are shown below MA = 0 RE * 16 – 5 * 8 – 3 * 12 = 0 RE = 4.75 kN Fy = 0 RE + RA – 5– 3 = 0 RA = 3.25 kN G C D E O F 4 m 2 m 6 m X

EXAMPLES of Trusses: Lecture 7 Example 3: In the following truss, find the force in member (EB). Solution Notice that no single cut will provide the answer. Hence, it is best to consider section (a-a and b-b). MA = 0 RC * 8 – 1000 * 6 – 1000 * 4 – 3000 * 2 = 0 RC = 2000 N Fy = 0 RA + RC – 1000 – 1000 – 3000 - 1000 = 0 RA = 4000 N Taking the moment about joint (B), to find (FED), as shown in below figure: MB = 0 1000 * 4 + 3000 * 2 – 4000 * 4 + FED * sin30o * 4 = 0 FED = 3000 N (compression)

Lecture 7 Continue Example 3: From joint (E) to find (FEB), as shown in below figure: Fx = 0 FEF . cos30o– 3000 cos30o = 0 FEF = 3000 N (compression) Fy = 0 FEF . Sin30o + 3000 . sin30o - 1000 - FEB = 0 FEF = 2000 N (Tension)