Use the matrix formulation of the stiffness method to compute the stiffness matrix,

nodal displacements, reactions, and member end forces in the truss shown in Figure $2.$ You

may edit the provided Excel spreadsheet $$HW$7\_$Prob$2\_$spreadsheet.xlsm$$ to arrive at the

solutions by populating the highlighted cells using the given problem data. The global DOFs

have been numbered in the spreadsheet already.

Assume $=29000$ for all members. All bar areas are $=1\mathrm{.}5$

$2$

except members $4$ and

$5$ which have $=0\mathrm{.}5$

$2$

Note

a$.$ All members are axial members so only horizontal DOFs are to be considered.

b$.$ Only showing the matrix equation will suffice for the final part. No need to solve for

unknown displacements and reactions. However, feel free to compute them to get an$(40$ Points$)$ Use the unit displacement approach to develop the structural stiffness matrix for

the structure shown in Figure $1,$ assuming that the axial stiffness of all three members are

identical, i$.$e$.(\frac{AE}{L}{)}_1=(\frac{AE}{L}{)}_2=(\frac{AE}{L}{)}_3=150\frac{k}{i}n.$ Then report the force$-$displacement matrix

equation that you need to solve to calculate the joint displacements. Partition the matrix

equation based on unconstrained and restrained degrees of freedom, and highlight the

components $F_u,R_r,{}_u,{}_r,K_{},K_{ur},K_{ru}$ and $K_{rr}.$ In this equation, show the constraints on

${}_r.$

Note

a$.$ All members are axial members so only horizontal DOFs are to be considered.

b$.$ Only showing the matrix equation will suffice for the final part. No need to solve for

unknown displacements and reactions. However, feel free to compute them to get an

extra credit of $10$ points!