CIVL3310 STRUCTURAL ANALYSIS Chapter 4: Internal Loadings Developed in Structural Members CIVL3310 STRUCTURAL ANALYSIS Professor CC Chang

Internal loadings at a cross section M V N M V Sign Convention + - +x +y Coordinates

Example 4.1 Sign Convention + -

Force, Shear and Bending Moment + M+dM V+dV V M dx C D VC VD

Force, Shear and Bending Moment P V-P V dx P V V-P x Shear force moves toward negative direction Mo + M-Mo M dx Mo M-Mo M x Moment moves toward Negative direction

Shear Force & Bending Moment Diagram L/2 +P/2 V -P/2 +PL/4 curvature +M -M M M Plotted on the tensile side +PL/4 Need to know deflection shape qualitatively

Shear Force & Bending Moment Diagram Structure under loads Slope of V = load Shear force diagram Slope of M = V Bending moment diagram Qualitative deflection shape Bending moment diagram (plotted on the tensile side)

Shear & Moment Diagrams for a Beam Sign Convention + -

Example 4.8 PL Moment plotted on the tensile side

Examples Chapter 4: Internal Loadings Developed in Structural Members Structural Analysis 7th Edition © 2009 Pearson Education South Asia Pte Ltd

Example 4.8 Draw shear force and bending moment diagrams

Solution 9m

Reflection: What Have You Learnt?