Chapter 5: Deformation

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Chapter 5 Deformation
Knowing is not enough we must apply. Willing is
not enough we must do. Johann Wolfgang von
Goethe
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Example 5.1
Figure 5.1 Cantilevered beam with concentrated
force applied at free end. Used in Example 5.1.
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Deflection by Singularity Functions
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Force on Simply Supported Beam
Figure 5.2 Free-body diagram of force anywhere
between simply-supported ends. (a) Complete bar
(b) portion of bar.
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Cantilever with Step Load
Figure 5.3 Cantilevered bar with unit step
distribution over part of bar. (a) Loads and
deflection acting on cantilevered bar (b)
free-body diagram of forces and moments acting on
entire bar (c) free-body diagram of forces and
moments acting on portion of bar.
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Cantilever with Concentrated Force
Figure 5.4 Cantilevered bar with other end
simply-supported and with concentrated force
acting anywhere along bar. (a) Sketch of
assembly (b) free-body diagram of entire bar
(c) free-body diagram of part of bar.
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Beam Deflections
Table 5.1 Deflection for three different
situations when one end is fixed and one end is
free and two different situations of simply
supported ends.
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Cantilever with Moment
Figure 5.5 Bar fixed at one end and free at
other with moment applied to free end and
concentrated force at any distance from free end.
(a) Complete assembly (b) free-body diagram
showing effect of concentrated force (c)
free-body diagram showing effect of moment.
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Stress Elements
Figure 5.6 Element subjected to normal stress.
Figure 5.7 Element subjected to shear stress.
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Strain Energy
Table 5.2 Strain energy for four types of
loading.
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Castiglianos Theorem
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Cantilever with Concentrated Force
Figure 5.8 Cantilevered bar with concentrated
force acting distance b from free end. (a)
Coordinate system and important points shown (b)
fictitious force shown along with concentrated
force.
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Linkage System
Figure 5.9 Linkage system arrangement. (a)
Entire assembly (b) free-body diagram of forces
acting at point A.
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Example 5.10
Figure 5.10 Cantilevered bar with 90 bend acted
upon by horizontal force at free end.