Table 1. Stresses and Deflections in Beams Table 1. (Continued) Stresses and Deflections in Beams
Stresses
Deflections
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 22. — Continuous Beam, with Two Equal Spans, Uniform Load s Zl W l x l x 2 4 1 = − − ^ a h k Maximum stress at point A, Z Wl 8 y
Maximum deflection is at x = 0.5785 l , and is EI Wl 185 3 Deflection at center of span, EI Wl 192 3 Deflection at point of greatest negative stress, at x = 5 ∕ 8 l is EI Wl 187 3
EIl Wx l x l x 48 3 2 2 − − ^ ^ h
h
=
Stress is zero at x = 1 ∕ 4 l Greatest negative stress is at x = 5 ∕ 8 l and is, 128 9 − Z Wl
Total Load on Each Span, W
x x A
3 W 8
3 W 8
l
l
5 W 4
Case 23. — Continuous Beam, with Two Equal Spans, Equal Loads at Center of Each
Between point A and load, s Z W l x 16 3 11 = − ^ h Between point B and load, s 16 5 =− Z Wv
Maximum stress at 16 3 Stress is zero at x l 11 3 = Greatest negative stress at center of span, Z Wl 32 5 − point A , Z Wl
Between point A and load, y EI Wx l = − ^ Between point B and load, y EI Wv l =
Maximum deflection is at v = 0.4472 l , and is
Wl 10733 3
x 96 9 11 2
h
. EI
Deflection at load,
W
B W
B
A
3
768 7
EI Wl
v 96 3 5 2 2 − ^
h
x x
1 2
1 2
1 2
1 2
l
l
5 W 16
11 W 16
5 W 16
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