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Lecture 6(E)_Zeb (1).pptx

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Engnr Kami Zeb
Engnr Kami Zeb

This document provides an overview of analyzing frames and machines. It begins with the objectives and in-class activities, which include drawing free body diagrams, determining joint and support forces, and solving practice problems. It then defines frames and machines, explaining that frames are stationary structures that support external loads while machines contain moving parts. The document teaches that for equilibrium, both internal and external forces must be considered. It provides an example of solving for unknown forces in a frame by drawing free body diagrams and applying equations of equilibrium. It concludes with quizzes to test comprehension.

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FRAMES AND MACHINES (Section 6.6) Today¡¯s Objectives: Students will be able to: a) Draw the free body diagram of a frame or machine and its members. b) Determine the forces acting at the joints and supports of a frame or machine. In-Class Activities: ?Reading quiz ? Applications ? Analysis of a frame/machine ?Concept quiz ? Group problem solving ? Attention quiz
Introduction 6 - 2 ? For the equilibrium of structures made of several connected parts, the internal forces as well the external forces are considered. ? In the interaction between connected parts, Newton¡¯s 3rd Law states that the forces of action and reaction between bodies in contact have the same magnitude, same line of action, and opposite sense. ? Three categories of engineering structures are considered: a) Trusses: formed from two-force members, i.e., straight members with end point connections and forces that act only at these end points. b) Frames: contain at least one multi-force member, i.e., member acted upon by 3 or more forces. c) Machines: structures containing moving parts designed to transmit and modify forces.
Provided a frame or machine contains no more supports or members than are necessary to prevent its collapse, the forces acting at the joints and supports can be determined by applying the equations of equilibrium to each of its members. Once these forces are obtained, it is then possible to design the size of the members, connections, and supports using the theory of mechanics of materials and an appropriate engineering design code.
APPLICATIONS Frames are commonly used to support various external loads. How is a frame different than a truss? How can you determine the forces at the joints and supports of a frame?
APPLICATIONS (continued) Machines, like these above, are used in a variety of applications. How are they different from trusses and frames? How can you determine the loads at the joints and supports? These forces and moments are required when designing the machine members.
FRAMES AND MACHINES: DEFINITIONS Frames and machines are two common types of structures that have at least one multi-force member. (Recall that trusses have nothing but two-force members). Frames are generally stationary and support external loads. Machines contain moving parts and are designed to alter the effect of forces.
READING QUIZ 1. Frames and machines are different as compared to trusses since they have ___________. A) only two-force members B) only multiforce members C) at least one multiforce member D) at least one two-force member 2. Forces common to any two contacting members act with _______ on the other member. A) equal magnitudes but opposite sense B) equal magnitudes and the same sense C) different magnitudes but opposite sense D) different magnitudes but the same sense
STEPS FOR ANALYZING A FRAME or MACHINE 1. Draw the FBD of the frame or machine and its members, as necessary. Hints: a) Identify any two-force members, b) Forces on contacting surfaces (usually between a pin and a member) are equal and opposite, and, c) For a joint with more than two members or an external force, it is advisable to draw a FBD of the pin. 2. Develop a strategy to apply the equations of equilibrium to solve for the unknowns. Problems are going to be challenging since there are usually several unknowns. A lot of practice is needed to develop good strategies. FAB FAB Pin B
EXAMPLE Given: The wall crane supports an external load of 700 lb. Find: The force in the cable at the winch motor W and the horizontal and vertical components of the pin reactions at A, B, C, and D. Plan: a) Draw FBDs of the frame¡¯s members and pulleys. b) Apply the equations of equilibrium and solve for the unknowns.
EXAMPLE ?+ ? FY = 2 T ¨C 700 = 0 T = 350 lb FBD of the Pulley E T T E 700 lb Necessary Equations of Equilibrium:
EXAMPLE (continued) ? + ? FX = CX ¨C 350 = 0 CX = 350 lb ? + ? FY = CY ¨C 350 = 0 CY = 350 lb ? + ? FX = ¨C BX + 350 ¨C 350 sin 30¡ã = 0 BX = 175 lb ? + ? FY = BY ¨C 350 cos 30¡ã = 0 BY = 303.1 lb A FBD of pulley B BY BX 30¡ã 350 lb 350 lb B A FBD of pulley C C 350 lb CY CX 350 lb
EXAMPLE (continued) Please note that member BD is a two- force member. + ? MA = TBD sin 45¡ã (4) ¨C 303.1 (4) ¨C 700 (8) = 0 TBD = 2409 lb ? + ? FY = AY + 2409 sin 45¡ã ¨C 303.1 ¨C 700 = 0 AY = ¨C 700 lb ? + ? FX = AX ¨C 2409 cos 45¡ã + 175 ¨C 350 = 0 AX = 1880 lb A FBD of member ABC AX AY A 45¡ã TBD B 175 lb 303.11 lb 700 lb 350 lb 4 ft 4 ft
EXAMPLE (continued) At D, the X and Y component are ? + DX = ¨C2409 cos 45¡ã = ¨C1700 lb ? + DY = 2409 sin 45¡ã = 1700 lb A FBD of member BD 45¡ã 2409 lb B 2409 lb D
CONCEPT QUIZ 1. The figures show a frame and its FBDs. If an additional couple moment is applied at C, then how will you change the FBD of member BC at B? A) No change, still just one force (FAB) at B. B) Will have two forces, BX and BY, at B. C) Will have two forces and a moment at B. D) Will add one moment at B.
2. The figures show a frame and its FBDs. If an additional force is applied at D, then how will you change the FBD of member BC at B? A) No change, still just one force (FAB) at B. B) Will have two forces, BX and BY, at B. C) Will have two forces and a moment at B. D) Will add one moment at B. CONCEPT QUIZ (continued) ? D
GROUP PROBLEM SOLVING Given: A frame and loads as shown. Find: The reactions that the pins exert on the frame at A, B and C. Plan: a) Draw a FBD of members AB and BC. b) Apply the equations of equilibrium to each FBD to solve for the six unknowns. Think about a strategy to easily solve for the unknowns.
GROUP EXAMPLE (continued) + ? MA = BX (0.4) + BY (0.4) ¨C 1000 (0.2) = 0 + ? MC = BX (0.4) + BY (0.6) + 500 (0.2) = 0 BY = 0 and BX = 500 N Equating moments at A and C to zero, we get: FBDs of members AB and BC: BY B BX 0.4m 500N C 0.2m 0.4m CY A X A B BY BX 1000N AY 45? 0.2m 0.2m
? + ? FX = AX ¨C 500 = 0 ; AX = 500 N ? + ? FY = AY ¨C 1000 + 500 = 0 ; AY = 500 N Consider member BC: ? + ? FX = 500 ¨C CX = 0 ; CX = 500 N ? + ? FY = CY ¨C 500 = 0 ; CY = 500 N GROUP EXAMPLE (continued) Applying EofE to bar AB: FBDs of members AB and BC: BY B BX 0.4m 500N C 0.2m 0.4m CY A X A B BY BX 1000N AY 45? 0.2m 0.2m
ATTENTION QUIZ 1. When determining the reactions at joints A, B, and C, what is the minimum number of unknowns for solving this problem? A) 3 B) 4 C) 5 D) 6 2. For the above problem, imagine that you have drawn a FBD of member AB. What will be the easiest way to directly solve for the first unknown? A) ? MC = 0 B) ? MB = 0 C) ? MA = 0 D) ? FX = 0
Lecture 6(E)_Zeb (1).pptx

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Lecture 6(E)_Zeb (1).pptx

  • 1. FRAMES AND MACHINES (Section 6.6) Today¡¯s Objectives: Students will be able to: a) Draw the free body diagram of a frame or machine and its members. b) Determine the forces acting at the joints and supports of a frame or machine. In-Class Activities: ?Reading quiz ? Applications ? Analysis of a frame/machine ?Concept quiz ? Group problem solving ? Attention quiz
  • 2. Introduction 6 - 2 ? For the equilibrium of structures made of several connected parts, the internal forces as well the external forces are considered. ? In the interaction between connected parts, Newton¡¯s 3rd Law states that the forces of action and reaction between bodies in contact have the same magnitude, same line of action, and opposite sense. ? Three categories of engineering structures are considered: a) Trusses: formed from two-force members, i.e., straight members with end point connections and forces that act only at these end points. b) Frames: contain at least one multi-force member, i.e., member acted upon by 3 or more forces. c) Machines: structures containing moving parts designed to transmit and modify forces.
  • 3. Provided a frame or machine contains no more supports or members than are necessary to prevent its collapse, the forces acting at the joints and supports can be determined by applying the equations of equilibrium to each of its members. Once these forces are obtained, it is then possible to design the size of the members, connections, and supports using the theory of mechanics of materials and an appropriate engineering design code.
  • 4. APPLICATIONS Frames are commonly used to support various external loads. How is a frame different than a truss? How can you determine the forces at the joints and supports of a frame?
  • 5. APPLICATIONS (continued) Machines, like these above, are used in a variety of applications. How are they different from trusses and frames? How can you determine the loads at the joints and supports? These forces and moments are required when designing the machine members.
  • 6. FRAMES AND MACHINES: DEFINITIONS Frames and machines are two common types of structures that have at least one multi-force member. (Recall that trusses have nothing but two-force members). Frames are generally stationary and support external loads. Machines contain moving parts and are designed to alter the effect of forces.
  • 7. READING QUIZ 1. Frames and machines are different as compared to trusses since they have ___________. A) only two-force members B) only multiforce members C) at least one multiforce member D) at least one two-force member 2. Forces common to any two contacting members act with _______ on the other member. A) equal magnitudes but opposite sense B) equal magnitudes and the same sense C) different magnitudes but opposite sense D) different magnitudes but the same sense
  • 8. STEPS FOR ANALYZING A FRAME or MACHINE 1. Draw the FBD of the frame or machine and its members, as necessary. Hints: a) Identify any two-force members, b) Forces on contacting surfaces (usually between a pin and a member) are equal and opposite, and, c) For a joint with more than two members or an external force, it is advisable to draw a FBD of the pin. 2. Develop a strategy to apply the equations of equilibrium to solve for the unknowns. Problems are going to be challenging since there are usually several unknowns. A lot of practice is needed to develop good strategies. FAB FAB Pin B
  • 9. EXAMPLE Given: The wall crane supports an external load of 700 lb. Find: The force in the cable at the winch motor W and the horizontal and vertical components of the pin reactions at A, B, C, and D. Plan: a) Draw FBDs of the frame¡¯s members and pulleys. b) Apply the equations of equilibrium and solve for the unknowns.
  • 10. EXAMPLE ?+ ? FY = 2 T ¨C 700 = 0 T = 350 lb FBD of the Pulley E T T E 700 lb Necessary Equations of Equilibrium:
  • 11. EXAMPLE (continued) ? + ? FX = CX ¨C 350 = 0 CX = 350 lb ? + ? FY = CY ¨C 350 = 0 CY = 350 lb ? + ? FX = ¨C BX + 350 ¨C 350 sin 30¡ã = 0 BX = 175 lb ? + ? FY = BY ¨C 350 cos 30¡ã = 0 BY = 303.1 lb A FBD of pulley B BY BX 30¡ã 350 lb 350 lb B A FBD of pulley C C 350 lb CY CX 350 lb
  • 12. EXAMPLE (continued) Please note that member BD is a two- force member. + ? MA = TBD sin 45¡ã (4) ¨C 303.1 (4) ¨C 700 (8) = 0 TBD = 2409 lb ? + ? FY = AY + 2409 sin 45¡ã ¨C 303.1 ¨C 700 = 0 AY = ¨C 700 lb ? + ? FX = AX ¨C 2409 cos 45¡ã + 175 ¨C 350 = 0 AX = 1880 lb A FBD of member ABC AX AY A 45¡ã TBD B 175 lb 303.11 lb 700 lb 350 lb 4 ft 4 ft
  • 13. EXAMPLE (continued) At D, the X and Y component are ? + DX = ¨C2409 cos 45¡ã = ¨C1700 lb ? + DY = 2409 sin 45¡ã = 1700 lb A FBD of member BD 45¡ã 2409 lb B 2409 lb D
  • 14. CONCEPT QUIZ 1. The figures show a frame and its FBDs. If an additional couple moment is applied at C, then how will you change the FBD of member BC at B? A) No change, still just one force (FAB) at B. B) Will have two forces, BX and BY, at B. C) Will have two forces and a moment at B. D) Will add one moment at B.
  • 15. 2. The figures show a frame and its FBDs. If an additional force is applied at D, then how will you change the FBD of member BC at B? A) No change, still just one force (FAB) at B. B) Will have two forces, BX and BY, at B. C) Will have two forces and a moment at B. D) Will add one moment at B. CONCEPT QUIZ (continued) ? D
  • 16. GROUP PROBLEM SOLVING Given: A frame and loads as shown. Find: The reactions that the pins exert on the frame at A, B and C. Plan: a) Draw a FBD of members AB and BC. b) Apply the equations of equilibrium to each FBD to solve for the six unknowns. Think about a strategy to easily solve for the unknowns.
  • 17. GROUP EXAMPLE (continued) + ? MA = BX (0.4) + BY (0.4) ¨C 1000 (0.2) = 0 + ? MC = BX (0.4) + BY (0.6) + 500 (0.2) = 0 BY = 0 and BX = 500 N Equating moments at A and C to zero, we get: FBDs of members AB and BC: BY B BX 0.4m 500N C 0.2m 0.4m CY A X A B BY BX 1000N AY 45? 0.2m 0.2m
  • 18. ? + ? FX = AX ¨C 500 = 0 ; AX = 500 N ? + ? FY = AY ¨C 1000 + 500 = 0 ; AY = 500 N Consider member BC: ? + ? FX = 500 ¨C CX = 0 ; CX = 500 N ? + ? FY = CY ¨C 500 = 0 ; CY = 500 N GROUP EXAMPLE (continued) Applying EofE to bar AB: FBDs of members AB and BC: BY B BX 0.4m 500N C 0.2m 0.4m CY A X A B BY BX 1000N AY 45? 0.2m 0.2m
  • 19. ATTENTION QUIZ 1. When determining the reactions at joints A, B, and C, what is the minimum number of unknowns for solving this problem? A) 3 B) 4 C) 5 D) 6 2. For the above problem, imagine that you have drawn a FBD of member AB. What will be the easiest way to directly solve for the first unknown? A) ? MC = 0 B) ? MB = 0 C) ? MA = 0 D) ? FX = 0

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