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 15. — Fixed at One End, Supported at the Other, Uniform Load
Maximum stress at point of fixture, Z Wl 8 Stress is zero at x = 1 ∕ 4 l . Greatest negative stress is at x = 5 ∕ 8 l and is 128 9 − Z Wl
Maximum deflection is at x = 0.5785 l , and is EI Wl 185 3 Deflection at center, EI Wl 192 3 Deflection at point of greatest negative stress, at x = 5 ∕ 8 l is EI Wl 187 3
Zl W l x l x 2 4 1 − − ^ a h
EIl Wx l x l x 48 3 2 2 − − ^ ^ h
s
y
k
h
=
=
Total Load W
3 16
Wl
x
W 5
l
16
5 8
W
Case 16. — Fixed at One End, Free but Guided at the Other, Uniform Load s Z Wl l x l x 3 1 2 1 2 = − + ` j & 0 Maximum stress, at y
Maximum deflection, at free end, EI Wl 24 3
EIl Wx l x 24 2 2 − ^ h
2
Total Load W
support, Z Wl 3
=
Wl 3
Stress is zero at x = 0.4227 l Greatest negative stress, at free end, Z Wl 6 −
Wl 6
x
l
W
Case 17. — Fixed at One End, Free but Guided at the Other, with Load s Z W l x = − a k Stress at support,
Maximum deflection, at free end,
Z Wl 2
2 1
EI Wx l x 12 3 2 2 − ^ h
y
=
Wl 2
Wl
3
W
EI
Z Wl
12
Stress at free end, 2 − These are the maximum stresses and are equal and opposite. Stress is zero at center.
x
Wl 2
l
W
Made with FlippingBook - Share PDF online