Civil Engineering Mechanics & Structures

Analyze plane stress conditions using Mohr's circle to determine principal stresses, maximum shear stress, and stresses on inclined planes.

Solve problems involving strain energy in axially loaded members under gradual, sudden, and impact loading conditions.

Calculate bending stresses in beams with rectangular, circular, I, T, and composite/flitched sections.

Design beams of uniform strength for constant maximum bending stress.

Calculate and plot shear stress distribution across rectangular, circular, I, and T cross-sections using the shear formula (τ = VQ/Ib).

Solve beam deflection problems with discontinuous loading using Macaulay's method.

Solve beam deflection and slope problems using Mohr's moment-area theorems.

Determine deflection and slope in beams (including those with variable EI) using the conjugate beam method.

Calculate deflections in determinate beams and trusses using the unit load (virtual work) method.

Analyze solid, hollow, stepped, and composite shafts under torsion to find stresses, angle of twist, strain energy, and power transmitted.

Analyze the stability of columns using Euler's, Rankine's, and Secant formulas for various end conditions and loading eccentricities.

Apply Castigliano's theorems to determine deflections and rotations in determinate structures (beams, frames, trusses).

Analyze indeterminate beams (propped, fixed, continuous) using the method of consistent deformation (force method).

Analyze indeterminate pin-jointed trusses (up to 2 degrees) using the method of consistent deformation (force method).

Compute fixed-end moments (FEMs) for standard loading cases on prismatic beams (point loads, UDL, couples, settlement).

Analyze continuous beams and portal frames (with/without sway), including support settlement, using the slope-deflection method.

Analyze continuous beams and non-sway rigid frames using the moment distribution method.

Construct Influence Line Diagrams (ILDs) for reactions, shear force, and bending moment in determinate beams using the Muller-Breslau Principle.

Determine the maximum shear force and bending moment at a section of a beam under a series of moving loads (UDL, single/multiple point loads).

Determine the absolute maximum bending moment in a simply supported beam traversed by a system of moving concentrated loads.

Construct ILDs for member forces in simply supported pin-jointed trusses to find maximum forces under moving loads.

Analyze three-hinged arches to determine reactions, normal thrust, radial shear, and bending moment under various loading conditions.

Analyze two-hinged and fixed arches to determine reactions and draw bending moment diagrams.

Evaluate the effects of rib shortening and temperature changes on the behavior of two-hinged and fixed arches.

Formulate and apply the force (flexibility) matrix method to analyze indeterminate beams and rigid frames.

Formulate and apply the displacement (stiffness) matrix method to analyze indeterminate beams and rigid frames.

Apply the theory of plastic bending to calculate shape factor and plastic moment capacity for various cross-sections.

Determine the collapse load of beams and simple frames using the static (equilibrium) method.

Determine the collapse load of beams and portal frames (with and without sway) using the kinematic (mechanism) method.

Calculate the product of inertia and determine the orientation of principal axes for a given cross-section.

Analyze stresses in beams subjected to unsymmetrical bending by locating the neutral axis and calculating bending stresses.