Handbook of Civil Engineering Calculations

The deviation of A from a tangent to the elastic curve through B is numerically equal

to the static moment of the area of the MI(EI) diagram within the interval AB with respect

to A. This tangential deviation is measured normal to the unstrained position of the beam.

Draw the elastic curve and the MI(EI) diagram as shown in Fig. 37.

2. Calculate the deviation t 1 of B from the tangent through A

Thus, J 1 = moment of MBC about BC = NL/(2EI) = NL^2 /(6EI). Also, (^6) L = I 1 IL =
NL/(6EI).

3. Determine the right-hand slope in an analogous manner


4. Compute the distance to the section where the slope is zero

Area MED = area MBC(x/L)^2 = Nx^1 J(TEIL); (^0) E = B 1 - area MED = NL/(6EI) -
Nx^2 /(2EIL) = Q;x = L/3Q5.

5. Evaluate the maximum deflection
   Evaluate ymax by calculating the deviation t 2 of A from the tangent through E' (Fig. 37).
   Thus area MED = O 1 = NL/(6EI); ymax = t 2 = NL/(6EI)](2x/3) = [NL/(6EI)][(2L/(3 x 3°^5 )]

• M,^2 /(9£Y3°^5 ), as before.

CONJUGATE-BEAM METHOD OF

DETERMINING BEAM DEFLECTION

The overhanging beam in Fig. 38 is loaded in the manner shown. Compute the deflection

at C.

Calculation Procedure:

1. Assign supports to the conjugate beam
   If a conjugate beam of identical span as the given beam is loaded with the MI(EI) diagram

(a) Elastic curve

(b) M/EI diagram

FIGURE 37