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SHEAR FORCE & BENDING MOMENT MR. VISHAL VASISTHA ASSISTANT PROFESSOR (ME) DRONACHARYA COLLEGE, GURGAON

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SHEAR FORCE & BENDING MOMENT INTRODUCTION TYPES OF BEAM AND LOAD SHEAR FORCE AND BENDING MOMENT

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INTRODUCTION Devoted to the analysis and the design of beams Beams – usually long, straight members In most cases – load are perpendicular to the axis of the beam Transverse loading causes only bending (M) and shear (V) in beam

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TYPES OF LOAD AND BEAM The transverse loading of beam may consist of Concentrated loads, P1, P2, unit (N) Concentrated loads, P1, P2, unit (N) Distributed loads, w, unit (N/m) Distributed loads, w, unit (N/m)

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TYPES OF LOAD AND BEAM (MAY-2003) Beams are classified to the way they are supported Several types of beams are shown below L shown in various parts in figure is called ‘span’

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DETERMINATIONS OF SF & & BM The Shear & bending moment diagram will be obtained by determining the values of V and M at selected points of the beam

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DETERMINATIONS OF SF & & BM The Shear V & bending moment M at a given point of a beam are said to be positive when the internal forces and couples acting on each portion of the beam are directed as shown in figure below The shear at any given point of a beam is positive when the external forces (loads and reactions) acting on the beam tend to shear off the beam at that point as indicated in figure below

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DETERMINATIONS OF SF & & BM The bending moment at any given point of a beam is positive when the external forces (loads and reactions) acting on the beam tend to bend the beam at that point as indicated in figure below

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POINTS TO BE REMEMBERED WHILE CONSTRUCTING SF & BM DIAGRAM (+) ve values of SF & BM above BASE line and (-) ve values below At vertical load, SF diagram ↑ or ↓ suddenly SF diagram is ↔ b/w two vertical loads or no load section while BM diagram is inclined In case of UDL, SF diagram is inclined and BM curve BM at free end of cantilever & supports of SSB is zero BM diagram is always inclined or curve For a cantilever beam, always start calculation from free end

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SF & BM DIAGRAM FOR CANTILEVER BEAM A cantilever 1.5 m long is loaded with a UDL of 2 KN/m run over a length of 1.25 m from the free end. It also carries a point load of 3kN at a distance of 0.25 m from the free end. Draw the S.F. and B.M. diagrams of the cantilever.

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