Page 74 - Civil Engineering Formulas

R
aL nP
1 2 P n(n + 2) n + 1
P (5n 2 + 10n + 6) (n + 1) 3
L 2 R = L 2 (For n an even number)
aL PL 8
P (For n an even number)
P
W = np aL P n(n + 2) (For n an odd number)
P L Load Shear Moment c L Elastic curve (f)
aL P
P PL 3 384EI
L 2 aL nP P L 2
P maL odd number)
1 2 (n + 1)(For n an 5n 2 + 10n + 1 n + l
aL R =
1 n + 1 R m(n – m + 1) n + 1 PL 8 n(n + 2) n + 1 PL 3 384EI
a = PL 2 PL 2 24EI

P
R = P
kL
k(3 – 4k 2 ) Elastic-curve equations for prismatic beams: (d) Shears, moments, and deflections for a concentrated load at midspan of a simply supported
L′′ 2
P k(3x′ – 3x′ 2 – k 2 )
(1 – 2k)L L Load Shear PkL Moment PL 3 24EI Elastic curve (e) prismatic beam. (e) Shears, moments, and deflections for two equal concentrated loads on a simply supported prismatic beam. (f) Shears, moments, and deflec-

P PL 3 6EI
L 2 x(3k – 3k 2 – x 2 )
kL k(1 – k) x′ (k < x′ < (1 – k))
R = P xL (x < k) PxL
PL 3 6EI PL 2 2EI
P

P/2 tions for several equal loads equally spaced on a simply supported prismatic beam. (Continued)
P
1 2
R =
L 2
PL 3 48EI

L Load Shear PL 4 Moment c L Elastic curve
P (d)
x(3 – 4x 2 )
L 2
P xL 1 2
1 2 x < xPL
R = 1 2 PL 3 48EI PL 2 16EI FIGURE 2.3
P/2

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