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Unformatted text preview: INTERNAL INTERNAL FORCES FORCES Shear Force and Bending Moment Shear Force and Bending Moment Equations and Diagrams Equations and Diagrams LEARNING OBJECTIVES LEARNING OBJECTIVES Be able to draw shear force and Be able to draw shear force and bending moment diagrams for bending moment diagrams for beams beams PREREQUISITE KNOWLEDGE PREREQUISITE KNOWLEDGE Units of measurement Units of measurement Trigonometry concepts Trigonometry concepts Rectangular component concepts Rectangular component concepts Equilibrium of forces in 2D Equilibrium of forces in 2D Internal force concepts Internal force concepts STRESSES AND STRAINS STRESSES AND STRAINS Stress is defined as load divided by the Stress is defined as load divided by the crosssectional area on which it acts. crosssectional area on which it acts. Strain is defined as the change in length divided by the original length. Stress = σ = Q/A Strain = ε = ΔL/L STRESSES AND STRAINS STRESSES AND STRAINS Stress = σ = Q/A Q Q A = πr 2 L ΔL Strain = ε = ΔL/L STRESSES AND STRAINS STRESSES AND STRAINS Stress = σ = Q/A Q Q A = πr 2 L ΔL Strain = ε = ΔL/L STRESSES AND STRAINS STRESSES AND STRAINS Stress = σ = Q/A Q Q A = πr 2 L ΔL Strain = ε = ΔL/L σ ε Δσ Δε Young’s Modulus = Δσ/Δε If Q increases gradually SHEAR FORCE AND BENDING MOMENT DIAGRAMS Shear force diagram or SFD is a graphical representation of the vertical shear force (V) along a structural member Bending moment diagram or BMD is a graphical representation of the bending moment (M) along a structural member SIGN CONVENTION OF SHEAR FORCE AND BENDING MOMENT The internal shear force is considered positive if it causes clockwise rotation of the structural member under consideration as shown below. Positive Negative SIGN CONVENTION OF SHEAR FORCE AND BENDING MOMENT The internal bending moment is considered positive if it causes compression of the top fiber of the structural member under consideration as shown below. Positive Moment Negative Moment Tension at Bottom Tension at top STEPS FOR THE INTERNAL SHEAR FORCE DIAGRAM 1. Draw FBD of the entire structure and calculate the support reactions 2. Calculate the internal shear force along the member under consideration from left to right. The shear force is equal to the integral of the externally applied...
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This note was uploaded on 07/26/2009 for the course CE 221 taught by Professor Buch during the Spring '08 term at Michigan State University.
 Spring '08
 Buch

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