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problem4_sol

# problem4_sol - 22.314/1.56/2.084/13.14 Fall 2006 Problem...

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22.314/1.56/2.084/13.14 Fall 2006 Problem Set IV Solution 1. The stress due to force F is uniform with a value of σ y / 2 as shown in Figure (a). The stress due to pure bending in elastic regime is linearly symmetric as shown in Figure (b) In elastic regime, combination of force and moment will give a linear stress distribution with a maximum value achieved at z = h/ 2 . Thus when yielding begins, as shown in Figure (c) σ = σ y σ y / 2 = σ y / 2 (a) (c) h/2 -h/2 z h/2 -h/2 y /2 z y z h/2 -h/2 y z 0 -h/2 h/2 z y (b) (d) The moment for reaching the yield at a local space can be calculated. The moment shown in the figure is counter clockwise, therefore: 1 σ y h 2 h M 1 = 2 × ( ) × ( ) × 3 × ( ) × b 2 2 2 2 1 M 1 = σ y bh 2 12 When further increasing the magnitude of moment, the yielding zone in lower beam will further extend but the maximum stress remains σ y as elastic perfect plastic material property

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is assumed. The upper beam become compressed and will also reach the yielding at a certain moment. This situation
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problem4_sol - 22.314/1.56/2.084/13.14 Fall 2006 Problem...

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