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Hamrock Fundamentals of Machine Elements

Example 5.1

Figure 5.1 Cantilevered beam with concentrated force applied at

free end. Used in Example 5.1.

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Hamrock Fundamentals of Machine Elements

Deflection by Singularity Functions

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Figure 5.2 Free-body diagram of force

anywhere between simply-supportedends. (a) Complete bar; (b) portion of

bar.

Force on Simply Supported Beam

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Figure 5.3 Cantilevered bar with unit

step distribution over part of bar. (a)

Loads and deflection acting on

cantilevered bar; (b) free-bodydiagram of forces and moments acting

on entire bar; (c) free-body diagram of

forces and moments acting on portion

of bar.

Cantilever with Step Load

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Figure 5.4 Cantilevered bar with other

end simply-supported and with

concentrated force acting anywherealong bar. (a) Sketch of assembly; (b)

free-body diagram of entire bar; (c)

free-body diagram of part of bar.

Cantilever with

Concentrated Force

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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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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) Completeassembly; (b) free-body diagram

showing effect of concentrated force;

(c) free-body diagram showing effect

of moment.

Cantilever with Moment

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Figure 5.6 Element subjected to

normal stress.

Figure 5.7 Element subjected

to shear stress.

Stress Elements

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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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Hamrock Fundamentals of Machine Elements

Figure 5.8 Cantilevered bar

with concentrated force acting

distance b from free end. (a)

Coordinate system andimportant points shown; (b)

fictitious force shown along

with concentrated force.

Cantilever with

Concentrated Force

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Hamrock Fundamentals of Machine Elements

Figure 5.9 Linkage system arrangement. (a) Entire assembly; (b) free-

body diagram of forces acting at point A.

Linkage System

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Hamrock Fundamentals of Machine Elements

Example 5.10

Figure 5.10 Cantilevered bar with 90 bend acted upon by horizontal

force at free end.