Practical Application

P$6\mathrm{.}34.$ Computer study of a two$-$hinged arch. The objec$-$

tive is to establish the difference in response of

a parabolic arch to $(1)$ uniformly distributed

loads and $(2)$ a single concentrated load.

$($a$)$ The arch in Figure P$6\mathrm{.}34$ supports a roadway con$-$

sisting of simply supported beams connected to the arch

by high$-$strength cables with area $A=2$ in$.{?}^2$ and

$E=26,000$ ksi. $($Each cable transmits a dead load from

the beams of $36$ kips to the arch.$)$ Determine the reactions,

the axial force, shear, and moment at each joint of the

arch, and the joint displacements. Plot the deflected

shape. Represent the arch by a series of straight segments

between joints. The arch has a constant cross section with

$A=24$ in$.{?}^2,I=2654$ in$.{?}^4,$ and $E=29,000$ksi.

$($b$)$ Repeat the analysis of the arch if a single $48-$kip

vertical load acts downward at joint $18.$ Again, deter$-$

mine all the forces acting at each joint of the arch, the

joint displacements, etc., and compare results with those

in $($a$).$ Briefly describe the difference in behavior.