Deflection Calculations

Case 1: Outrigger located at top, z = L

The rotation compatibility condition at z = L (see Fig. 3.19) can be written as q w - q s = q L (3.1)

where qW = rotation of the cantilever at z = L due to a uniform lateral load W, in radians. qs = rotation due to spring restraint located at z = L, in radians. The negative sign for qs in Eq. 3.1 indicates that the rotation of the cantilever due to the spring stiffness is in a direction opposite to the rotation due to external load. qL = final rotation of the cantilever at z = L, in radians.

Figure 3.19. Outrigger at top, z = L.

For a cantilever with uniform moment of inertia I and modulus of elasticity E subjected to uniform horizontal load W,

W 6EI

If M1 and K1 represent the moment and stiffness of the spring located at z = L, Eq. (3.1) can be rewritten as

6EI EI K1

WL3/6EI

The resulting deflection A1 at the building top can be obtained by superposing the deflection of the cantilever due to external uniform load W, and the deflection due to the moment induced by the spring, thus

A load

A spring

WL4

ml2

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