The deflection (δ) at the center of a simply supported beam under a central point load (P) is given by δ = PL^3 / 48EI.

The moment of inertia (I) for a rectangular beam section is given by I = bh^3/12, where b is the base and h is the height.

The moment of inertia I of a rectangular section is given by I = bh^3/12, where b is the width and h is the height.

The reaction at each support of a simply supported beam with a uniform load (W) is given by R = WL/2.

The shear force (V) at a section x from the left end of a simply supported beam with a point load (W) at one end is given by V = W - wx, where w is the distributed load per unit length.

For a simply supported beam with a point load W at the center, the maximum bending moment M is given by M = WL/4.

The maximum bending moment for a simply supported beam with a central point load is given by M = WL^2/8.

The maximum bending moment (M) for a simply supported beam with a point load (W) at the center is given by M = WL/4, where L is the length of the beam.

The maximum bending moment (M) for a simply supported beam with a point load (W) at the center and length (L) is given by M = WL/4.

The maximum deflection (δ) for a cantilever beam with a point load (P) at the free end is given by δ = PL^3/3EI.

The maximum shear force occurs just to the left of the load, which is equal to the point load, hence it is 15 kN.

The moment of inertia (I) for a rectangular beam section is given by I = (b * h^3) / 12, where b is the width and h is the height of the section.

The primary advantage of using the stiffness method is its ability to handle indeterminate structures effectively.

The primary advantage of using the virtual work method is its applicability to indeterminate structures, allowing for the calculation of deflections and internal forces.

The primary advantage of using trusses in construction is lower material usage while maintaining structural integrity.

The primary assumption made in the Euler-Bernoulli beam theory is that plane sections remain plane after deformation, along with the material being isotropic and elastic.

The primary purpose of the stiffness method is to analyze indeterminate structures by relating displacements to forces through stiffness matrices.

The moment distribution method is primarily used to analyze indeterminate structures by distributing moments to achieve equilibrium.

The primary purpose of using a shear diagram in beam analysis is to visualize the distribution of shear forces along the length of the beam.

The primary purpose of using a truss in structural design is to reduce material usage while maintaining strength and stability, as trusses efficiently distribute loads.

Factors of safety are used in structural design to account for uncertainties in material properties, loads, and environmental conditions.

The primary purpose of using the stiffness method in structural analysis is to analyze indeterminate structures by relating displacements to forces.

The relationship between bending moment (M) and shear force (V) in a beam is given by M = ∫V dx, where the integral is taken along the length of the beam.

The relationship between shear force V and bending moment M in a beam is given by V = dM/dx, where x is the distance along the beam.

The relationship is given by V = dM/dx, meaning the shear force is the derivative of the bending moment with respect to the position along the beam.

In the elastic range, the deflection of a beam is directly proportional to the load applied, according to Hooke's Law.

The deflection of a beam is inversely proportional to the moment of inertia (I); as I increases, deflection decreases.

The deflection of a beam is inversely proportional to the moment of inertia (I); as I increases, deflection decreases.

The stiffness of a beam is directly proportional to its moment of inertia (I); a larger I results in greater stiffness.

The stiffness (k) of a beam is defined as the ratio of the load (P) applied to the deflection (δ) produced, thus k = P / δ.