P$2.$ This problem explores the structural analysis of a truss. In the design of highway bridge structures and crane

structures, engineers are often required to compute the member forces and support reactions in planar truss structures.

The analysis of cantilever truss structures is governed by the following principles:

At each joint, the sum of internal and external forces in the horizontal and vertical directions must equal zero.

The sum of external forces and support reactions in the horizontal and vertical directions must equal zero.

For the entire structure and all possible substructures, the sum of moments must equal zero.

The truss elements can only carry axial forces, with tensile axial forces being positive and compressive axial

forces being negative.

All the joints are pinned $($the joints cannot transfer moments; only axial forces from the truss elements$).$

The truss is statically determinate $($axial forces can be computed without knowledge of material properties$)$

The figure shows a six$-$bar cantilever truss carrying $10$ kN loads at joints B and C $.$ Nodes A and E are rigidly attached to a

wall.

Write the equilibrium equations in the horizontal and

vertical directions for each of the five joints.

For example, at joint $A,$ using $F$ for force and $R$ for

reaction:

x$-$component: $F_1+F_{5x}+R_{Ax}=0$

y$-$component: $F_{5y}+R_{Ay}=0$

Also, $F_{5x}=F_{5y}=F_{5}cos(45)=\frac{\sqrt[\phantom{2}]{2}}{2}{F}_5=\frac{\sqrt[\phantom{2}]{2}}{2}\frac{\sqrt[\phantom{2}]{2}}{\sqrt[\phantom{2}]{2}}{F}_5=\frac{1}{\sqrt[\phantom{2}]{2}}{F}_5$

While at joint B: $F_1=F_2$ and $F_4=10(kN)$

P$2.$ This problem explores the structural analysis of a truss. In the design of highway bridge structures and crane

structures, engineers are often required to compute the member forces and support reactions in planar truss structures.

The analysis of cantilever truss structures is governed by the following principles:

At each joint, the sum of internal and external forces in the horizontal and vertical directions must equal zero.

The sum of external forces and support reactions in the horizontal and vertical directions must equal zero.

For the entire structure and all possible substructures, the sum of moments must equal zero.

The truss elements can only carry axial forces, with tensile axial forces being positive and compressive axial

forces being negative.

All the joints are pinned $($the joints cannot transfer moments; only axial forces from the truss elements$).$

The truss is statically determinate $($axial forces can be computed without knowledge of material properties$)$

The figure shows a six$-$bar cantilever truss carrying $10$ kN loads at joints B and C $.$ Nodes A and E are rigidly attached to a

wall.

Write the equilibrium equations in the horizontal and

vertical directions for each of the five joints.

For example, at joint $A,$ using $F$ for force and $R$ for

reaction:

x$-$component: $F_1+F_{5x}+R_{Ax}=0$

y$-$component: $F_{5y}+R_{Ay}=0$

Also, $F_{5x}=F_{5y}=F_{5}cos(45)=\frac{\sqrt[\phantom{2}]{2}}{2}{F}_5=\frac{\sqrt[\phantom{2}]{2}}{2}\frac{\sqrt[\phantom{2}]{2}}{\sqrt[\phantom{2}]{2}}{F}_5=\frac{1}{\sqrt[\phantom{2}]{2}}{F}_5$

While at joint B: $F_1=F_2$ and $F_4=10(kN)$