ENGR 220 Section 12.1~12.2

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ENGR 220Section 12.112.2
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Deflection of Beams and Shafts
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Sign Convention
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Coordinates v, x and y
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Curvature related to v and x Non-Linear Second
Order Differential Equation. ELASTICA
Assumption slope is very small Engineering
Constraints Neglect (dv/dx)2 term.
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Deflection Equations
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• Boundary Conditions

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Example 12.1
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Determine equations of elastic curve. Specify
slope at B and deflection at C
12.26
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Multiple Loadings 4 Moment equations
8 constants of
Integration 2
Boundary Conditions
6 Continuity Conditions
Advanced Methods Discontinuity Functions
and Singularity Functions Moment Area Method
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The fence board weaves between three posts. If
the posts remain in the same line, determine
maximum bending stress in the board. The board
has a width of 6 in and thickness of 0.5 in. E
1.6 x 103 ksi. Assume displacement of each end
relative to center of the board is 3 in.
12.13
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Method of Superposition
A steel bar is supported by two springs at its
ends A and B. Each spring has a stiffness of 15
kip/ft and is originally unstretched. If the bar
is loaded with a force of 3 kip at point C,
determine the vertical displacement of the force.
Neglect the weight of the bar. Est 29 (103)
ksi. I 12 in4
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A picture is taken of a man performing a pole
vault. The minimum radius of curvature of the
pole is estimated by measurement to be 4.5
meters. If the pole diameter is 40 mm, and is
made of glass reinforced plastic for which E
131 GPa, determine the maximum bending stress in
the pole.