Page 82 - Civil Engineering Formulas
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38 CHAPTER TWO
l
P
R R = V = P
M max (at fixed end) = Pl
x
M x = Px
Δ max (at free end) = Pl 3
V 3EI
P 3 2 3
Shear Δ x = (2l – 3l x + x )
6EI
M max
Moment
(p)
FIGURE 2.3 Elastic-curve equations for prismatic beams: (p) Cantilever beam—con-
centrated load at free end. (Continued)
l
x P
R = V = P
R R 2
Pl
l l M max (at center and ends) =
2 2 P 8
M when x < l = (4x – l)
V x 2 8
Shear V Δ max (at center) = Pl 3
192EI
l Px 2
4 M max Δ x = 48EI (3l – 4x)
M max M max
Moment
(q)
FIGURE 2.3 Elastic-curve equations for prismatic beams: (q) Beam fixed at both
ends—concentrated load at center. (Continued)
