The stiffness (k) of a beam is directly proportional to its moment of inertia (I), meaning k ∝ I.

The stiffness of a beam is inversely proportional to its deflection; as stiffness increases, deflection decreases.

The shear force (V) at a section located at a distance 'x' from the left end of a simply supported beam with a point load (W) at the center is V = W/2 - x.

The shear force (V) just to the left of a point load (P) on a simply supported beam is equal to V = P.

Shear Force at midpoint = 10 kN (load at one end) - 0 kN (no load on the other end) = 10 kN.

The shear force at the midpoint of a simply supported beam with a point load at one end is 0, as the load is not applied at that point.

The shear force at the fixed support of a cantilever beam with a uniform load (w) is equal to the total load, which is WL.

The shear force (V) at the support of a simply supported beam with a point load (P) at one end is equal to P.

The shear force (V) at the supports of a simply supported beam with a point load (P) at the center is V = P/2.

The shear force at the support of a simply supported beam with a uniform load is WL/2.

The shear force at the supports of a simply supported beam with a uniform load w is V = wL/2.

Total Load = Dead Load + Live Load = 15 kN + 10 kN = 25 kN.

The Stiffness Method is commonly used to analyze indeterminate structures by relating displacements to forces.

The Virtual Work Method is commonly used to analyze the deflection of indeterminate structures.

A statically indeterminate structure has more unknowns than equilibrium equations, requiring additional methods for analysis.

A fixed beam is statically indeterminate because it has more supports than necessary to maintain equilibrium.