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Page 1 Shear Force and Bending Moment Diagrams A 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 • A Shear Force Diagram (SFD) indicates how a force applied perpendicular to the axis (i.e., parallel to cross-section) of a beam is transmitted along the length of that beam. • A Bending Moment Diagram (BMD) will show how the applied loads to a beam create a moment variation along the length of the beam. Types of Supports (a) Roller Support - resists vertical forces only i Rb (b) Hinge support or pin connection - resists horizontal and vertical forces Page 2 Shear Force and Bending Moment Diagrams A 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 • A Shear Force Diagram (SFD) indicates how a force applied perpendicular to the axis (i.e., parallel to cross-section) of a beam is transmitted along the length of that beam. • A Bending Moment Diagram (BMD) will show how the applied loads to a beam create a moment variation along the length of the beam. Types of Supports (a) Roller Support - resists vertical forces only i Rb (b) Hinge support or pin connection - resists horizontal and vertical forces 7777777 A ____ t R'y Resists horizontal and vertical forces • Hinge and roller supports are called as simple supports (c) Fixed support or built-in end and vertical forces and moment • 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 S im p ly supported beams (2) Cantilever beam: Beam fixed at one end and free at other ?TTTTT T r _____________ (3) Overhanging beam Page 3 Shear Force and Bending Moment Diagrams A 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 • A Shear Force Diagram (SFD) indicates how a force applied perpendicular to the axis (i.e., parallel to cross-section) of a beam is transmitted along the length of that beam. • A Bending Moment Diagram (BMD) will show how the applied loads to a beam create a moment variation along the length of the beam. Types of Supports (a) Roller Support - resists vertical forces only i Rb (b) Hinge support or pin connection - resists horizontal and vertical forces 7777777 A ____ t R'y Resists horizontal and vertical forces • Hinge and roller supports are called as simple supports (c) Fixed support or built-in end and vertical forces and moment • 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 S im p ly supported beams (2) Cantilever beam: Beam fixed at one end and free at other ?TTTTT T r _____________ (3) Overhanging beam L (4) Continuous beam: More than two supports Shear Force The resultant force which is in upward direction and is towards the L.H.S of the X-sectlon is +ve Shear Force The resultant force which is in the downward direction and is towards the R.H.S of the X-section is +ve Shear Force. The resultant force which are in the downward direction and is on the L.H.S of the X-section is -ve Shear Force. The resultant force which are in upward direction and is on the R.H.S of the X-sectlon Is -ve Shear Force. Shear force has a tendency to slide the surface, it acts parallel to surface. Y.F = 0 — * xm Page 4 Shear Force and Bending Moment Diagrams A 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 • A Shear Force Diagram (SFD) indicates how a force applied perpendicular to the axis (i.e., parallel to cross-section) of a beam is transmitted along the length of that beam. • A Bending Moment Diagram (BMD) will show how the applied loads to a beam create a moment variation along the length of the beam. Types of Supports (a) Roller Support - resists vertical forces only i Rb (b) Hinge support or pin connection - resists horizontal and vertical forces 7777777 A ____ t R'y Resists horizontal and vertical forces • Hinge and roller supports are called as simple supports (c) Fixed support or built-in end and vertical forces and moment • 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 S im p ly supported beams (2) Cantilever beam: Beam fixed at one end and free at other ?TTTTT T r _____________ (3) Overhanging beam L (4) Continuous beam: More than two supports Shear Force The resultant force which is in upward direction and is towards the L.H.S of the X-sectlon is +ve Shear Force The resultant force which is in the downward direction and is towards the R.H.S of the X-section is +ve Shear Force. The resultant force which are in the downward direction and is on the L.H.S of the X-section is -ve Shear Force. The resultant force which are in upward direction and is on the R.H.S of the X-sectlon Is -ve Shear Force. Shear force has a tendency to slide the surface, it acts parallel to surface. Y.F = 0 — * xm V—qdx— (V +dV)=0 d r dx ~9 Only for distributed load not for point load. Bending Moment Any moment produced by forces acting on the beam must be balance by an equal opposite moment produced by internal forces acting in beam at the section. This moment is called bending moment. v \ \ / = 0 — M — qdx dx z ~ {V + d V )d x+ M + dm = 0 dU Fix = V => Ma — M A = f V dx Only for distributed and concentrated load not for couple. • The necessary internal forces to keep the segment of the beam in equilibrium are £ F X = 0 =>P Z F y = 0 =>V Z F z = 0 = > M Resultant moment on the L.H.S of the X-section is C.W, then it is a positive B.M A Resultant moment on the R.H.S postion of the X-section is C C W. then it may be considered as positive B.M Page 5 Shear Force and Bending Moment Diagrams A 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 • A Shear Force Diagram (SFD) indicates how a force applied perpendicular to the axis (i.e., parallel to cross-section) of a beam is transmitted along the length of that beam. • A Bending Moment Diagram (BMD) will show how the applied loads to a beam create a moment variation along the length of the beam. Types of Supports (a) Roller Support - resists vertical forces only i Rb (b) Hinge support or pin connection - resists horizontal and vertical forces 7777777 A ____ t R'y Resists horizontal and vertical forces • Hinge and roller supports are called as simple supports (c) Fixed support or built-in end and vertical forces and moment • 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 S im p ly supported beams (2) Cantilever beam: Beam fixed at one end and free at other ?TTTTT T r _____________ (3) Overhanging beam L (4) Continuous beam: More than two supports Shear Force The resultant force which is in upward direction and is towards the L.H.S of the X-sectlon is +ve Shear Force The resultant force which is in the downward direction and is towards the R.H.S of the X-section is +ve Shear Force. The resultant force which are in the downward direction and is on the L.H.S of the X-section is -ve Shear Force. The resultant force which are in upward direction and is on the R.H.S of the X-sectlon Is -ve Shear Force. Shear force has a tendency to slide the surface, it acts parallel to surface. Y.F = 0 — * xm V—qdx— (V +dV)=0 d r dx ~9 Only for distributed load not for point load. Bending Moment Any moment produced by forces acting on the beam must be balance by an equal opposite moment produced by internal forces acting in beam at the section. This moment is called bending moment. v \ \ / = 0 — M — qdx dx z ~ {V + d V )d x+ M + dm = 0 dU Fix = V => Ma — M A = f V dx Only for distributed and concentrated load not for couple. • The necessary internal forces to keep the segment of the beam in equilibrium are £ F X = 0 =>P Z F y = 0 =>V Z F z = 0 = > M Resultant moment on the L.H.S of the X-section is C.W, then it is a positive B.M A Resultant moment on the R.H.S postion of the X-section is C C W. then it may be considered as positive B.M A negative B.M ¦ negative B.M A Differential equations of equilibrium P(x)kg per unit length 1111 1 i ^ rrmr \X— So the differential equations would be: 1 4 AV d V 4*->0 A X “ X 7. AM dM l i m — = - i - = ~ v A t— >0 A x “ x ,we can write V d - V c = - \ Pdx From equation d y d x -M ,we can write M D - M c = - \ V d xRead More
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