Analyze the frame. Show detailed calculation $($Necessary$).$

$4\mathrm{.}18$ Example. Figure $4-31$a shows a plane frame having two members, three

joints, six restraints, and three degrees of freedom. This frame is to be analyzed by

the methods given in the previous section. For this purpose, assume that the cross$-$

sectional area $A_x$ and the moment of inertia $I_Z$ are constant throughout the structure.

Assume also that the parameters in the problem have the following numerical values:

$E=10,000$ksiL$=100in.,I_Z=1000in.{?}^4,P=10kips{A}_x=10in.{?}^2$

For this frame the material is aluminum, and units of kips, inches, and radians are

used throughout the analysis."

A numbering system for members, joints, and displacements is given in Fig.

$4-31$b$,$ which shows the restrained structure. The sequence for numbering the joints

is selected in such a manner that the matrices in the analysis do not require rearrange$-$

ment.

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