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Shear and Moment Diagrams in Beams: Graphical Representation and Design Insights

Shear and moment diagrams visually represent internal forces in beams, aiding identification of maximum shear and bending moments crucial for structural design. This tutorial covers general expressions for internal forces, drawing diagrams for various load types, and analyzing examples to understand discontinuities and combined loading effects.

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Shear and Moment Diagrams in Beams: Graphical Representation and Design Insights

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  1. 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

  2. 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

  3. 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

  4. 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

  5. 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

  6. Example 2 (con’d) ES2501: Statics/Unit 21-6: Internal Forces in Beams Diagrams: Shear diagram Moment diagram Parabola

  7. 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

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