Trusses Lecture 7 Truss is a structure composed

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. v Each member of a truss is usually of uniform cross section along its length. Calculation are usually based on following assumption: Ø The loads and reactions act only at the joint. Ø Weight of the individual members can be neglected. Ø 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. Ø Joints are modeled by smooth pin connections. 1

Analysis of Trusses Lecture 7 Truss Analysis Internal equilibrium External equilibrium To find the force in each member To find the reaction forces Method of joints Method of sections External Equilibrium: to find the reaction forces, follow the below steps: 1. Draw the FBD for the entire truss system. 2. Determine the reactions. Using the equations of (2 D) which states: 2

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: 1. Draw the FBD for the entire truss system. 2. Determine the reactions. Using equations of (2 D) which states: the 3. Choose the joint, and draw FBD of a joint with at least one known force and at most two unknown forces. 4. Using the equation of (2 D) which states: 5. The internal forces are determined. 6. Choose another joint. 3

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: 1. Draw the FBD for the entire truss system. 2. Determine the reactions. Using equations of (2 D) which states: the 3. Choose the section, and draw FBD of that section, shows how the forces replace the sectioned members. 4. Using the equation of (2 D) which states: 5. The internal forces are determined. 6. Choose another section or joint. 4

Analysis of Trusses 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: 1. 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. 5

Analysis of Trusses Lecture 7 Analysis of trusses (Zero-force members): Examples to follow: 2. 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 6

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. Ø Assume BC is in compression. 7

Lecture 7 EXAMPLES of Trusses: 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 å Fy = 0 å MA = 0 RE * 16 – 5 * 8 – 3 * 12 = 0 RE + RA – 5– 3 = 0 RE = 4. 75 k. N RA = 3. 25 k. N G F 2 m 6 m C D 4 m O E 4 m X 8

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). å MA = 0 RC * 8 – 1000 * 6 – 1000 * 4 – 3000 * 2 = 0 RC = 2000 N å Fy = 0 RA + RC – 1000 – 3000 - 1000 = 0 RA = 4000 N Taking the moment about joint (B), to find (FED), as shown in below figure: åMB = 0 1000 * 4 + 3000 * 2 – 4000 * 4 + FED * sin 30 o * 4 = 0 FED = 3000 N (compression) 9

Lecture 7 Continue Example 3: From joint (E) to find (FEB), as shown in below figure: å Fx = 0 FEF. cos 30 o– 3000 cos 30 o = 0 FEF = 3000 N (compression) å Fy = 0 FEF. Sin 30 o + 3000. sin 30 o - 1000 - FEB = 0 FEF = 2000 N (Tension) 10