Page 1 Solid Mechanics 1. Shear force and bending moment diagrams Internal Forces in solids Sign conventions · Shear forces are given a special symbol on y V 1 2 and z V · The couple moment along the axis of the member is given x M T = = Torque y z M M = =bending moment. Page 2 Solid Mechanics 1. Shear force and bending moment diagrams Internal Forces in solids Sign conventions · Shear forces are given a special symbol on y V 1 2 and z V · The couple moment along the axis of the member is given x M T = = Torque y z M M = =bending moment. Solid Mechanics We need to follow a systematic sign convention for systematic development of equations and reproducibility of the equations The sign convention is like this. If a face (i.e. formed by the cutting plane) is +ve if its outward normal unit vector points towards any of the positive coordinate directions otherwise it is –ve face · A force component on a +ve face is +ve if it is directed towards any of the +ve coordinate axis direction. A force component on a –ve face is +ve if it is directed towards any of the –ve coordinate axis direction. Otherwise it is –v. Thus sign conventions depend on the choice of coordinate axes. Shear force and bending moment diagrams of beams Beam is one of the most important structural components. · Beams are usually long, straight, prismatic members and always subjected forces perpendicular to the axis of the beam Two observations: (1) Forces are coplanar Page 3 Solid Mechanics 1. Shear force and bending moment diagrams Internal Forces in solids Sign conventions · Shear forces are given a special symbol on y V 1 2 and z V · The couple moment along the axis of the member is given x M T = = Torque y z M M = =bending moment. Solid Mechanics We need to follow a systematic sign convention for systematic development of equations and reproducibility of the equations The sign convention is like this. If a face (i.e. formed by the cutting plane) is +ve if its outward normal unit vector points towards any of the positive coordinate directions otherwise it is –ve face · A force component on a +ve face is +ve if it is directed towards any of the +ve coordinate axis direction. A force component on a –ve face is +ve if it is directed towards any of the –ve coordinate axis direction. Otherwise it is –v. Thus sign conventions depend on the choice of coordinate axes. Shear force and bending moment diagrams of beams Beam is one of the most important structural components. · Beams are usually long, straight, prismatic members and always subjected forces perpendicular to the axis of the beam Two observations: (1) Forces are coplanar Solid Mechanics (2) All forces are applied at the axis of the beam. Application of method of sections What are the necessary internal forces to keep the segment of the beam in equilibrium? x y z F P F V F M = = = 0 0 0 · The shear for a diagram (SFD) and bending moment diagram(BMD) of a beam shows the variation of shear Page 4 Solid Mechanics 1. Shear force and bending moment diagrams Internal Forces in solids Sign conventions · Shear forces are given a special symbol on y V 1 2 and z V · The couple moment along the axis of the member is given x M T = = Torque y z M M = =bending moment. Solid Mechanics We need to follow a systematic sign convention for systematic development of equations and reproducibility of the equations The sign convention is like this. If a face (i.e. formed by the cutting plane) is +ve if its outward normal unit vector points towards any of the positive coordinate directions otherwise it is –ve face · A force component on a +ve face is +ve if it is directed towards any of the +ve coordinate axis direction. A force component on a –ve face is +ve if it is directed towards any of the –ve coordinate axis direction. Otherwise it is –v. Thus sign conventions depend on the choice of coordinate axes. Shear force and bending moment diagrams of beams Beam is one of the most important structural components. · Beams are usually long, straight, prismatic members and always subjected forces perpendicular to the axis of the beam Two observations: (1) Forces are coplanar Solid Mechanics (2) All forces are applied at the axis of the beam. Application of method of sections What are the necessary internal forces to keep the segment of the beam in equilibrium? x y z F P F V F M = = = 0 0 0 · The shear for a diagram (SFD) and bending moment diagram(BMD) of a beam shows the variation of shear Solid Mechanics force and bending moment along the length of the beam. These diagrams are extremely useful while designing the beams for various applications. Supports and various types of beams (a) Roller Support – resists vertical forces only (b) Hinge support or pin connection – resists horizontal and vertical forces Hinge and roller supports are called as simple supports (c) Fixed support or built-in end Page 5 Solid Mechanics 1. Shear force and bending moment diagrams Internal Forces in solids Sign conventions · Shear forces are given a special symbol on y V 1 2 and z V · The couple moment along the axis of the member is given x M T = = Torque y z M M = =bending moment. Solid Mechanics We need to follow a systematic sign convention for systematic development of equations and reproducibility of the equations The sign convention is like this. If a face (i.e. formed by the cutting plane) is +ve if its outward normal unit vector points towards any of the positive coordinate directions otherwise it is –ve face · A force component on a +ve face is +ve if it is directed towards any of the +ve coordinate axis direction. A force component on a –ve face is +ve if it is directed towards any of the –ve coordinate axis direction. Otherwise it is –v. Thus sign conventions depend on the choice of coordinate axes. Shear force and bending moment diagrams of beams Beam is one of the most important structural components. · Beams are usually long, straight, prismatic members and always subjected forces perpendicular to the axis of the beam Two observations: (1) Forces are coplanar Solid Mechanics (2) All forces are applied at the axis of the beam. Application of method of sections What are the necessary internal forces to keep the segment of the beam in equilibrium? x y z F P F V F M = = = 0 0 0 · The shear for a diagram (SFD) and bending moment diagram(BMD) of a beam shows the variation of shear Solid Mechanics force and bending moment along the length of the beam. These diagrams are extremely useful while designing the beams for various applications. Supports and various types of beams (a) Roller Support – resists vertical forces only (b) Hinge support or pin connection – resists horizontal and vertical forces Hinge and roller supports are called as simple supports (c) Fixed support or built-in end Solid Mechanics The distance between two supports is known as “span”. Types of beams Beams are classified based on the type of supports. (1) Simply supported beam: A beam with two simple supports (2) Cantilever beam: Beam fixed at one end and free at other (3) Overhanging beam (4) Continuous beam: More than two supportsRead More

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