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Deflections and Slopes of Beams

Table 1. Deflections and slopes of cantilever beams

v = deflection in the y direction

(positive upward)

dv/dx = slope of the deflection curve

B = v(L) = deflection at end B of

the beam (downward)

B = angle of rotation at end B

of the beam (clockwise)

EI = constant

1

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Table 2. Deflections and slopes of simple beams

v = deflection in the y direction

(positive upward)

dv/dx = slope of the deflection curve

C = v(L/2) = deflection at midpoint C of

the beam (downward)

x1 = distance from support A to

point of maximum deflection

max = vmax = maximum deflection (downward)

A = angle of rotation at left-hand

end of the beam (clockwise)

B = angle of rotation at right-hand

end of the beam (counterclockwise)

EI = constant

1

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