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TR7_ENGR111A_2011C_MM (4)

TR7_ENGR111A_2011C_MM (4) - Calculating Internal Forces in...

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ENGR 111 Track A 1 Calculating Internal Forces in a Truss using Method of Joints. Zero-force Members. TR-7
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RAT 05_01 ENGR 111 Track A 2 Page Team Number RAT 02_02 Section Number Date Name Take a NEW clean sheet of paper and write Reminder: Individual work There are two problems on this RAT. Take 3 minutes to solve each of the problems.
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RAT 05_01 Estimate the Moment in the problem below. Can the truss below be in static equilibrium? Why or why not? (hint: what are the reaction forces at A and C) ENGR 111 Track A 3 20  lb A B C 30° 60° F = 10 N pivot 1 m
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ENGR 111 Track A 4 Learning Objectives In this module you will learn how to Calculate internal forces in truss members using Method of Joints Draw the free body diagram of the joints in a truss. Develop the equilibrium equations for a joint. Apply the equilibrium equations to find the unknown forces at a joint . Identify whether a member is in tension or compression.
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ENGR 111 Track A 5 Trusses: Internal Forces Links in a truss are 2-force members. The force on a truss link is called an axial force . If the force tends to lengthen the member it is called a tensile (tension) force . If the force tends to shorten the member it is called a compressive force . R E V I E W
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ENGR 111 Track A 6 Truss Links are in Equilibrium. Equal and Opposite Forces on the Joint! Link in TENSION : Force points away from the link (force stretches the link) Now think about how this link interacts with the joints: Newtons 3rd law implies forces are equal and opposite Link in COMPRESSION : Force points towards the link (force pushes on the link) Equilibrium implies forces on the link are equal and opposite . R E V I E W
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ENGR 111 Track A 7 Trusses: FBDs of Links (Bars) Draw the FBD for each bar. IGNORE GRAVITY. Remember 2-force members. There should be 3 FBDs! If you are unsure whether the bar is in tension or compression, assume tension . We will always assume that the bars are in tension! 20 lb A B C 30° 60° Fab Fab Fac Fac Fbc Fbc R E V I E W
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ENGR 111 Track A 8 Trusses: FBDs of Joints “Exploded view” of the truss ABC. Notice the forces at joints!! 20 lb A B C F AC F AC F BC F BC F AB F AB Ay By Bx F BC F BC F AB F AB F AC F AC
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ENGR 111 Track A 9 Internal Forces: Method of Joints How do we find the forces in the links? Three steps: 1. Start with finding the external reaction forces. Work with the truss as a whole: forget about the links for now (links are always in equilibrium!). Draw the FBD of the Truss, write down the equilibrium equations, solve for unknown external reactions. This part we know. 2. New: we need to “explode” the truss. We will work with joints only. Draw the FBD of the Joints: assume that all links are in tension; recall that links (bars) are 2-force members, hence forces act along the bars.
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