Handbook of Civil Engineering Calculations

7. Compute the horizontal displacement of one point
   relative to another
   Thus, EIk 2 = EIO^ = Pb(ac + ab/2).


8. Combine the computed displacements to obtain the absolute
   displacement
   Thus E7A = £/(A 2 - ^7A 1 ) = Pb(ac + ab/2 - c^2 /2); A = [Pb/(2EI)](2ac + ab- c^2 ).

Statically Indeterminate Structures

A structure is said to be statically determinate if its reactions and internal forces may be
evaluated by applying solely the equations of equilibrium and statically indeterminate if
such is not the case. The analysis of an indeterminate structure is performed by combining
the equations of equilibrium with the known characteristics of the deformation of the
structure.

SHEAR AND BENDING MOMENT OF A BEAM

ONA YIELDING SUPPORT

The beam in Fig. 41« has an EI value of 35 x 109 lb-in^2 (100,429 kN-m^2 ) and bears on a
spring at B that has a constant of 100 kips/in (175,126.8 kN/m); i.e., a force of 100 kips
(444.8 kN) will compress the spring 1 in (25.4 mm). Neglecting the weight of the mem-
ber, construct the shear and bending-moment diagrams.

( b) Force diagram

FIGURE 41

(a) Load on beam

(c) Shear diagram