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ES2501: Statics/Unit 21-1 : Graphical Representation of Internal Forces in Beams: Shear and Moment Diagrams. Introduction:. Shear and moment diagrams give a graphical representation of the internal forces in a beam as how the shear and bending moment
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ES2501: Statics/Unit 21-1: Graphical Representation of Internal Forces in Beams: Shear and Moment Diagrams Introduction: Shear and moment diagrams give a graphical representation of the internal forces in a beam as how the shear and bending moment distributed over the span of a bear. The maximum shear and bending moment can be easily identified for structural design. As the first step a general expression for the internal forces of a beam need to be found for ANY arbitrary position as a function of position. An arbitrary position designated by variable, x N(x) is zero in the case of loading is perpendicular to the axis of a straight beam Internal forces at ANY arbitrary position ss functions of a variable of x
ES2501: Statics/Unit 21-2: Internal Forces in Beams Example 1: Draw the shear and moment diagram for a simply-supported subjected to a point load. Support Reactions: General Expressions for Internal forces: Case I:for a typical cross-sectionI between points A and C, i.e. Note: this set of expressions apply for any position between A and C, i,e, ONLY
ES2501: Statics/Unit 21-3: Internal Forces in Beams Example 1 (con’d): General Expressions for Internal forces: Case 2:for a typical cross-sectionII between points C and B, i.e. Twotypical cross-sections are needed due to existence of the point load, P, which make the internal forces discontinuous and mathematically speaking, piecewise expressions for the Internal forces are necessary. Note: this set of expressions apply for any position between C and B, i,e, ONLY
Example 1 (con’d): Graphic Expressions for Internal forces: ES2501: Statics/Unit 21-4: Internal Forces in Beams Diagrams: Discontinuity of sudden drop/jump due to a point load
Example 2: Draw the shear and moment diagram for a simply-supported subjected to a uniformly-distributed load. ES2501: Statics/Unit 21-5: Internal Forces in Beams Statically-equivalent to the distributed load Support Reactions: General Expressions for Internal forces: (only one typical cross-section I needs to consider Statically-equivalent to the part of the distributed load
Example 2 (con’d) ES2501: Statics/Unit 21-6: Internal Forces in Beams Diagrams: Shear diagram Moment diagram Parabola
Example 3: Draw the shear and moment diagram for a simply-supported subjected to combined loading. ES2501: Statics/Unit 21-7: Internal Forces in Beams Results for Ponly Results for q0 only Results for combined P and q0 Shear diagram Moment diagram