A simply supported beam spans $L = 10 \text{ m}$. It is supported by a pin at $A$ (left end) and a roller at $B$ (right end). A vertical point load of $P = 50 \text{ kN}$ is applied at a distance of $4 \text{ m}$ from support $A$. Calculate the reactions at $A$ and $B$.

A cantilever beam of length $L = 6 \text{ m}$ is fixed at the left end ($A$) and free at the right end ($B$). It carries a uniformly distributed load of $w = 15 \text{ kN/m}$ over its entire length. Calculate the reactions at the fixed support $A$.

A beam is supported by a pin at $A$ ($x=0$) and a roller at $B$ ($x=8 \text{ m}$). The beam overhangs to the right to point $C$ ($x=10 \text{ m}$). It carries a point load of $40 \text{ kN}$ at $x=4 \text{ m}$, and a point load of $20 \text{ kN}$ at the overhang tip ($x=10 \text{ m}$). Find the reactions at $A$ and $B$.

A simple triangular truss consists of three members forming a right triangle. Member $AB$ is horizontal ($4 \text{ m}$), member $BC$ is vertical ($3 \text{ m}$), and member $AC$ is the hypotenuse ($5 \text{ m}$). It is pinned at $A$ and has a roller at $B$. A downward force of $100 \text{ kN}$ is applied at joint $C$. Find the internal force in member $AB$.

A Pratt roof truss has 6 horizontal panels of $3 \text{ m}$ each ($18 \text{ m}$ total span) and a height of $4 \text{ m}$. It is supported by a pin at the left and a roller at the right. Downward point loads of $50 \text{ kN}$ are applied at the bottom chord joints. Find the force in the top chord member located in the 3rd panel from the left.

Identify zero-force members in a complex truss to simplify analysis.

A cable is suspended between two supports $A$ and $B$ at the same elevation, spanning $20 \text{ m}$. A single point load of $100 \text{ kN}$ is applied at the midspan, causing a sag of $5 \text{ m}$. Find the maximum tension in the cable.

A suspension bridge main cable spans $100 \text{ m}$ horizontally between two towers of equal height. The cable carries a uniform horizontal load of $w = 20 \text{ kN/m}$ (representing the deck). The maximum sag in the center is $10 \text{ m}$. Find the horizontal tension ($H$).

Using the same suspension bridge cable from Example 2 (Span $100 \text{ m}$, load $20 \text{ kN/m}$, sag $10 \text{ m}$, $H = 2500 \text{ kN}$), calculate the maximum tension in the cable.

A symmetrical three-hinged parabolic arch has a span of $L = 40 \text{ m}$ and a rise (height) of $h = 10 \text{ m}$ to the central crown hinge. It is subjected to a vertical point load of $120 \text{ kN}$ located $10 \text{ m}$ horizontally from the left support. Calculate the horizontal thrust ($H$) at the supports.

A three-hinged semi-circular arch has a radius of $15 \text{ m}$. A uniform horizontal wind load of $5 \text{ kN/m}$ acts on the left half of the arch. Find the reactions at the base.

Using the symmetrical arch from Example 1, determine the internal shear force, axial force, and bending moment at a section $10 \text{ m}$ from the left support (directly under the $120 \text{ kN}$ load).