(Part A) Machinerys Handbook 31st Edition Pages 1-1484

Table 1. Stresses and Deflections in Beams Table 1. (Continued) Stresses and Deflections in Beams

Deflections

Stresses

General Formula for Stress at any Point

Stresses at Critical Points General Formula for Deflection at any Point a

Type of Beam

Deflections at Critical Points a

Case 10. — Fixed at One End, Uniform Load

Stress at support, Z Wl 2

Maximum deflection, at end, EI Wl 8 3

s Zl W l x 2 = − ^ h

EIl Wx l 24 2 2 2 2

2

l x + − ^ h 6 @ 2

y

=

Total Load W

Wl 2

If cross section is constant, this is the maximum stress.

x

l

W

Case 11. — Fixed at One End, Load at Other

Stress at support, Z Wl

Maximum deflection, at end, EI Wl 3 3

s Z W l x = − ^ h

y EI Wx l x 6 3 2 = − ^ h

If cross section is constant, this is the maximum stress.

W

Wl

x

l

W

Case 12. — Fixed at One End, Intermediate Load

Stress at support, Z Wl

Deflection at load, EI Wl 3 3 Maximum deflection, at end, EI Wl l b 6 2 3 2 + ^ h

Between support and load,

Between support and load, s Z W l x = − ^ h Beyond load, s = 0.

y EI Wx l x 6 3 2 = − ^ h

W

Wl

If cross section is constant, this is the maximum stress.

Beyond load,

x

v

y EI Wl v l 6 3 2 = − ^ h

l

b

W

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