机械设计手册.Machinery's.Handbook_.27th.Edition

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[机械设计手册（27版）美版].Machinery's.Handbook，.27th.EditionReaction at the Supports.-When a beam is loaded by verticalloads or forces， the sum of
the reactions at the supports equals the sum of the loads. In a simple beam， when the loads
are symmetrically placed with reference to the supports， or when the load is uniformly dis-tributed， the reaction at each end will equal one-half of the sum ofthe loads. When the
loads are not symmetrically placed， the reaction at each support may be ascertained from
the fact that the algebraic sum of the moments must equal zero. In the accompanying illus-tration， if moments are taken about the support to the left， then: R2×40 −8000 ×10 −
10，000 ×16 −20，000 ×20 0; R2
16，000 pounds. In the same way， moments taken about
the support at the right give R1
22，000 pounds.
The sum of the reactions equals 38，000 pounds， which is also the sum of the loads. If part
of the load is uniformly distributed over the beam， this part is first equally divided between
the two supports， or the uniform load may be considered as concentrated at its center of
gravity.
If metric SI units are used for the calculations， distances may be expressed in meters
or millimeters， providing the treatment is consistent， and loads in newtons. Note:If
the load is given in kilograms， the value referred to is the mass. A mass of Mkilograms
has a weight (applies a force) of Mgnewtons， where g approximately 9.81 meters
per second
2
.
Stresses and Deflections in Beams.-On the following pages Table 1gives an extensive
list of formulas for stresses and deflections in beams， shafts， etc. It isassumed that all the
dimensions are in inches， all loads in pounds， and all stresses in pounds per square inch.
The formulas are also valid using metric SI units， with all dimensions in millimeters，
all loads in newtons， and stresses and moduli in newtons per millimeter
2(N/mm
2
).
Note:A load due to the weight of a mass of Mkilograms is Mgnewtons， where g
approximately 9.81 meters per second
2
.In the tables:
Emodulus of elasticity of the material
Imoment of inertia of the cross-section of the beam