Module 3: Analysis of Statically Determinate Structures - Examples

A $10\text{ m}$ simply supported beam carries $P=50\text{ kN}$ at $4\text{ m}$ from the left support $A$. Find $A_y$ and $B_y$.

A $6.0\text{ m}$ cantilever carries $w=15\text{ kN/m}$ over its full length. Determine the vertical and moment reactions at the fixed support.

A beam segment from $x=0$ to $x=4\text{ m}$ carries $w=8\text{ kN/m}$ downward. If $V(0)=25\text{ kN}$ using the lesson sign convention, find $V(4)$.

Over a $5.0\text{ m}$ beam segment, shear varies linearly from $+20\text{ kN}$ to $-10\text{ kN}$. If $M(0)=12\text{ kN}\cdot\text{m}$, find $M(5)$.

An internal hinge separates a beam into left and right segments. The left segment has a known downward load of $30\text{ kN}$ and a support reaction of $18\text{ kN}$ upward. Determine the vertical hinge force acting on the left segment.

At an unloaded truss joint, members $AB$ and $BC$ are collinear and a third member $BD$ is non-collinear. No support reaction acts at the joint. Determine $F_{BD}$.

At a truss joint, a $100\text{ kN}$ downward load is resisted by a horizontal member and a diagonal member with a $3$-$4$-$5$ geometry. Find the diagonal force and the horizontal member force, assuming both unknown forces act away from the joint.

A truss section cuts three unknown member forces. Two of their lines of action intersect at point $O$. External loads on the isolated side create a net clockwise moment of $240\text{ kN}\cdot\text{m}$ about $O$. The third cut-member force $F$ has a perpendicular lever arm of $3.0\text{ m}$. Find $F$.

A cable spans $L=40\text{ m}$ with central sag $f=5.0\text{ m}$ and carries $w=6.0\text{ kN/m}$ uniformly per unit horizontal length. Determine the horizontal component of cable tension.

For the cable in Example 9, determine the support vertical reaction and the support tension magnitude.

A symmetric three-hinged arch spans $20\text{ m}$ with crown hinge rise $4.0\text{ m}$. A $60\text{ kN}$ point load acts at midspan directly over the crown. Determine the vertical reactions and horizontal thrust.