Chapter 2Symmetrical Bending System

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Lesson OutcomesAt the end of the lecture, students will be able toDefine beams and identify types of beams, their connections and loads.Apply the equilibrium conceptDraw free body diagram

Symmetrical Bending SystemBASIS FOR BEAM DESIGNBeams are structural members designed to support loadings perpendicular to their longitudinal axes.Under load, internal shear force and bending moment that vary from pt to pt along axis of beam.Axial stress is ignored in design, as its much smaller than the shear force and bending moment.A beam designed to resist shear and bending moment is designed on the basis of strength.

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A) Type of LoadsConcentrated load/Point loadKnife loadUniformly distributed load (udl)Varying linearly distributed loadTriangular load

Symmetrical Bending System

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Symmetrical Bending System

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Concentrated/point load

Uniformly distr. loadTriangular load

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Symmetrical Bending SystemB) Type of supports/connections

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C) Type of BeamsCantilever beam a beam which is fixed at one end and free at the other end.Simply supported beam a beam where both ends are supported or placed freely on the wall or columnOverhanging beam a beam that has one end overhanging, as in the cantilever but exceeds the support. Can also have both ends overhangingFixed beam a beam where both ends are fixed rigidly into the wallContinuous beam a beam that has more than two supports

Symmetrical Bending System

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Symmetrical Bending System

Cantilever beamSimply supported beam

Overhanging beam

orFixed beamContinuous beam

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Free Body Diagram (FBD)?Symmetrical Bending SystemPL (m)ABIdealized structureFBD external forcesL (m)

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Shear Force (V)Symmetrical Bending SystemPV1V2For equilibrium, V1 and V2 are equal in magnitude but opposite in direction.

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Bending Moment (M)Symmetrical Bending SystemFor equilibrium, M1 and M2 are equal in magnitude but opposite in direction.Note:Variations of Shear Force and Bending Moment along a beam can be visualised by Shear Force Diagram (SFD) and Bending Moment Diagram (BMD) respectively

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Common Notations (sign convention)Symmetrical Bending System

VNNMMV+The positive values for axial force, N, shear force, V, and bending moment, M

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Thank you

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