Page 73 - Handbook of Civil Engineering Calculations, Second Edition

1.56 STRUCTURAL STEEL ENGINEERING AND DESIGN

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 M/(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 M/(EI) diagram as shown in Fig. 37.
2. Calculate the deviation t 1 of B from the tangent through A
2
Thus, t 1 moment of ABC about BC [NL/(2EI)](L/3) NL /(6EI). Also, L t 1 /L
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 AED area ABC(x/L) Nx /(2EIL); E L area AED NL/(6EI)
2
2
0.5
2
Nx /(2EIL) 0; x L/3 .
5. Evaluate the maximum deflection
Evaluate y max by calculating the deviation t 2 of A from the tangent through E
(Fig. 37).
Thus area AED L NL/(6EI); y max t 2 NL/(6EI)](2x/3) [NL/(6EI)][(2L/(3
0.5
2
0.5
3 )] NL /(9EI3 ), 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 M/(EI) diagram
of the latter, the shear V
and bending moment M
of the conjugate beam are equal,

FIGURE 37