Mechanics of Materials Lab Lecture 2-4 Beam Mechanics of Materials Laboratory Sec. 3-4 Jiangyu Li University of Washington Jiangyu Li, University of Washington

Jiangyu Li, University of Washington Beam Jiangyu Li, University of Washington

Jiangyu Li, University of Washington Type of Supports Beam supported on a wall Beam-to-column connection Pole anchored to a concrete pier Jiangyu Li, University of Washington

Jiangyu Li, University of Washington Types of Beams Simply supported beam Cantilever beam Simply supported beam with overhang Jiangyu Li, University of Washington

Shear Force & Bending Moment Jiangyu Li, University of Washington

Jiangyu Li, University of Washington Sign Convention Jiangyu Li, University of Washington

Shear Force & Bending Moment Diagram Negative q Negative P Positive M0 Jiangyu Li, University of Washington

Shear Force & Bending Moment Diagram Jiangyu Li, University of Washington

Shear Force and Bending Moment Diagram Jiangyu Li, University of Washington

Jiangyu Li, University of Washington Deflection in Beam Jiangyu Li, University of Washington

Jiangyu Li, University of Washington Normal Stress in Beam How to identify the neutral axis? Jiangyu Li, University of Washington

Jiangyu Li, University of Washington Normal Stress Go through centroid ! Jiangyu Li, University of Washington

Jiangyu Li, University of Washington Shear Stress Jiangyu Li, University of Washington

Distribution of Shear Stress Jiangyu Li, University of Washington

Jiangyu Li, University of Washington Shear Stress Jiangyu Li, University of Washington

Jiangyu Li, University of Washington Shear Stress Jiangyu Li, University of Washington

Jiangyu Li, University of Washington Deflection of Beam Jiangyu Li, University of Washington

Jiangyu Li, University of Washington Deflection of Curve Jiangyu Li, University of Washington

Jiangyu Li, University of Washington Boundary Condition Jiangyu Li, University of Washington

Jiangyu Li, University of Washington Continuity Condition Jiangyu Li, University of Washington

Deflection by Bending Moment Equation Jiangyu Li, University of Washington

Deflection by Loading Equation Jiangyu Li, University of Washington

Deflection by Superposition Jiangyu Li, University of Washington

Strain Energy of Pure Bending Jiangyu Li, University of Washington

Strain Energy of Bending Jiangyu Li, University of Washington

Strain Energy of a Beam in Shear Rectangular: 1.2 Circular: 1.11 Thin-walled tubular, round: 2.00 Box section: 1.00 Structural section: 1.00 Jiangyu Li, University of Washington

Strain Energy of Bending Jiangyu Li, University of Washington

Castigliano’s Theorem When forces act on a elastic system subject to small displacements, the displacement corresponding to any force, collinear with the force, is equal to the partial derivative of the total strain energy with respect to that force. It can also be used to find the displacement when no force is applied at that point. Jiangyu Li, University of Washington

Modified Castigliano’s Theorem Jiangyu Li, University of Washington

Jiangyu Li, University of Washington Application Jiangyu Li, University of Washington

Jiangyu Li, University of Washington Inclined Load Notice the sign convention: positive Mz compress upper part, negative stress; positive My extend front part, positive stress! Jiangyu Li, University of Washington

Jiangyu Li, University of Washington Inclined Load Stress Neutral axis Jiangyu Li, University of Washington

Jiangyu Li, University of Washington Assignment Read Mechanics of Materials Lab Sec. 3 4.25(a,b,c), 4.26(a) posted online Jiangyu Li, University of Washington