Structural Analysis

Examine static determinacy and indeterminacy by comparing reaction counts to equilibrium equations, then apply compatibility for externally indeterminate cases. Learn pin joint conditions and the path to internal indeterminacy.

Identify internal determinants and apply DSI rules to classify beams, rigid jointed frames, and pin jointed frames as determinate or indeterminate, using r-s, C counts, and DSI.

Explore how adding hinges and links to plain frames yields hybrid structures, releasing forces to determine static indeterminacy using dsc, dsi, and forces released, with examples.

Explore static indeterminacy in frames and girders by calculating degree of indeterminacy for plain and hybrid structures, and compare determinate versus indeterminate systems with practical examples.

Learn about hybrid structures and static indeterminacy, and how hinges release forces (axial, shear, and moment) across joints, gusset plates, and links with practical examples.

Compute the degree of static indeterminacy for plain and hybrid plane frames and bow string girders, and contrast statically determinate and indeterminate structures.

Explains lack of fit in pin-jointed frames, shows how shortfalls cause strain in indeterminate structures, and contrasts determinate frames with no stress due to lack of fit.

Explore external and internal stability of pin-jointed frames and concurrent reaction forces, identify unstable and well-formed (perfect) configurations, and apply simple static indeterminacy formulas to assess rigidity.

Explore plane truss assumptions, including pin joints, loads acting at joints, axial forces only, and self-weight ignored, with zero-force member identification and compression-tension sign conventions.

Explore truss analysis using the method of joints and the method of section, with symmetry-based reactions, equilibrium forces, and identifying tensile and compressive member forces.

Use the method of section on a pin-jointed plain frame truss to cut sections, release a member force, and apply vertical, horizontal, and moment equilibrium.

Explains solving plane-frame truss problems using the method of sections, identifying zero-force members, and applying equilibrium and moment equations to isolate forces in specific members.

Learn to analyze plane frame trusses using the method of sections, identify zero-force members, and compute forces in key members such as cb, cd, be, and ab.

Apply the method of section to a truss, eliminate zero force members, compute vertical and horizontal reactions, and determine the force in the target member.

Explore the method of joints and the method of section for statically determinate planar trusses, comparing two and three equilibrium equations, and addressing zero force members and joint loading.

Explore rolling loads and influence lines on statically determinate structures, learning how moving unit loads shape reaction, shear, bending moment, and axial force through influence line diagrams.

Compute bending moment at section c of a simply supported beam under a moving unit load, determine reactions at A and B, and illustrate the influence line and moment diagram.

Explore influence line diagrams for cantilever beams, deriving reactions and shear and bending moment at key sections using unit loads, and learn a quick displacement-based shortcut for drawing these diagrams.

Analyze overhanging beams by constructing shear force and bending moment diagrams, determine support reactions, and apply similar triangles to compute key heights.

Use the influence line diagram on a simply supported beam with a roller load to find maximum reactions at A and B, and the maximum shear and moment at C.

Analyze a simply supported beam with a roller load to find the maximum bending moment at C using w(a(L-a)/L). Observe how load position alters shear and bending moment diagrams.

Analyze a beam with overhanging udl to compute maximum reactions at a and b, and then find shear force and bending moment at section c, including absolute maxima.

Explore moving-load problems on simply supported beams, deriving maximum bending moments and shear forces using influence lines, average loading, and sectioning techniques in structural analysis.

Determine the maximum bending moment due to moving wheel loads on a simply supported beam by locating the critical wheel at section c and summing load times distance to c.

Compute the center of gravity of the four rolling loads w1, w2, w3, w4 to locate the resultant and determine the absolute maximum bending moment for a non-specified section.

Explore case three and case four of rolling load systems, showing how equal, equidistant loads set the resultant and govern bending moments.

This lecture analyzes five moving loads on an 80 m simply supported beam, computes the load center, and determines the maximum bending moment location by evaluating four cases.

An overhang beam problem with two point loads of 100 and 150 kN five meters apart on a simply supported beam, determining reactions and maximum hogging and sagging moments.

Analyze maximum reactions and positive and negative shear forces for moving and wheel loads on simply supported and overhanging girders, including 12 m and double overhang cases.

Continue solving a cantilever beam problem by calculating bending moments at a and d and the shear force at d using unit-load analysis, and draw their diagrams.

analyze a beam with supports at a, b, c and a hinge at d to determine reactions and shear under a 2 kN/m, 3 m distributed load, using unit-load analysis.

Draw influence lines for reactions at A, B, and C; compute shear just to the right of B and bending moment one meter right of B on a hinged beam.

Explore influence lines for reactions at A and B and for shear force and bending moment at C on an eight‑meter simply supported beam with a moving unit moment.