Page 75 - Civil Engineering Formulas

(L 2 – L′ 2 )
(L + L′) 2
x′ 2
wL′x′
wL′ 2
x′L′
w
2
(L + L′) 2 (L – L′) 2
2L
2L
w
w
L′
R 2 =
R 2
wL′ 2
2
wL′
8L 2
w
R 1 = wLx
(L 2 – L′ 2 )
L′ 2
Shear
Load
L
1 – L′ 2
L 2
2L
w
w
(L 2 – L′ 2 – xL 2 )
R 1 =
xL
2
L
R 1
wx
2
P
P
xL
Load
Shear
L
PxL 1 – L L 2 Moment Moment wL′ (4L′ 2 – L 3 + 3L′ 3 ) 24EI PL 3 wL 2 x (2 – 3x + x 3 ) L 2 (1 – 2x 2 + x 2 ) –2L′ 2 (1 – x 2 ) 3EI 24EI PL 3 3EI Elastic curve Elastic curve (h) (i) Elastic-curve equations for prismatic beams
R = P
PL R PL
(L + L′)
PL′ 2 3EI
P
P 2(L + L′) – L′x′ (1 + x′)
x′L′
L′
Px′L′
PL′
P R 2 x(1 – x 2 ) length of a beam with overhang. (Continued)
L + L′ L Load Shear xPL′ PL′ 2 (1 – x′) 6EI Elastic curve (g)
R 2 = L PL′L 2 6EI
xL
P L Moment L 3 PL′L 2 3EI
R 1 = L′ 9 FIGURE 2.3
R 1 d max =
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