Structural Analysis I

Identify statically determinate beams and analyze them with free-body diagrams and the three static equilibrium equations, considering pin, roller, and fixed supports, cantilevers, and loads.

Explore stability and determinacy in trusses by applying equilibrium under varying loads, distinguishing external from internal stability, and using methods of joints to classify as statically determinate or indeterminate.

Analyze the stability and determinacy of rectangular frames used as building skeletons, applying static equilibrium to reveal degree of indeterminacy for rigid versus hinged connections.

Analyze beams with internal hinges by applying static equilibrium to each segment, distinguishing moment and shear splices, and determining support reactions and hinge forces.

analyze statically determinate two-dimensional trusses using the method of joints, determine support reactions, and compute each member’s axial force as tension or compression.

Apply the method of sections to analyze a K-truss, using cuts and a joint moment equation to determine forces, calculate support reactions, and solve for Fab, Fbc, and Fac.

Apply the method of sections to a truss, perform multiple cuts, and determine support reactions, then solve for member forces Fbc and Fcg using moment and equilibrium equations.

Apply the method of joints to analyze an exterior roof truss under dead load, identify zero-force members, compute support reactions, and use symmetry for efficient joint-by-joint results.

Explore how shear force and bending moment develop in beams, identify the neutral axis, and apply equilibrium equations to calculate internal forces in simply supported beams.

Compute shear force and bending moment for beams under uniform, triangular, and nonlinear distributed loads using equivalent concentrated loads and free-body diagrams, including simply supported and cantilever cases.

Derive and apply shear and moment equations for a statically determinate beam by writing piecewise V(x) and M(x) for left, middle, and right segments.

Derive shear and moment equations for a simply supported beam under triangular load, using a cut at x to obtain V(x) and M(x), and locate the maximum moment.

Derive shear and moment equations for a simply supported beam under a load split into rectangular and triangular parts, yielding piecewise V(x) and M(x) for 0–4 m and 4–10 m.

Draw moment diagrams from the shear diagram using area under the curve, starting at zero moment at a pin, to locate critical moment values on beams.

Compute the beam's shear and moment diagrams using support reactions, divide the load into segments, use areas under the load diagram, and draw the resulting curves.

Determine the beam’s shear and moment diagrams from area under the load diagram using support reactions, treating the beam as AB and BC, and identify the maximum moment at B.

Compute the beam's reaction forces via static equilibrium and draw the free-body diagram to create shear and moment diagrams using sign conventions and area methods.

draw shear and moment diagrams for a two-dimensional statically determinate steel–concrete canopy frame, using line diagrams, free-body analyses, and boundary conditions to compute reactions and generate segment diagrams.

This lecture introduces the double integration method to compute beam deflection by relating slope theta to dv/dx, M, and EI, deriving the deflection equation for cantilever and simply supported beams.

Apply the double integration method to find beam deflection by integrating M/EI twice, and use the slope equation theta(x)=dv/dx with boundary conditions at a cantilever to solve for C1, C2.

Apply the double integration method to obtain left and right deflection equations for a simply supported beam with piecewise moment, enforce boundary and continuity conditions, and locate the maximum deflection.

Apply the double integration method to derive v(x) for a tapered cantilever with a rectangular cross-section, where I(x)=I0(1+x/10)^3, and determine constants from v(10)=0 and theta(10)=0, noting maximum deflection at x=0.

Use the conjugate beam method to compute deflection in a simply supported beam by treating M/EI as a distributed load and reading the conjugate moment.

Apply the conjugate beam method to compute deflections under concentrated loads by loading the conjugate beam with the M/EI diagram and reading the moment at point A.

Explore reaction influence lines for statically determinate beams, showing how a unit moving load changes B’s reaction and scaling to actual loads in cantilever, simply supported, and hinged beams.

Explore drawing and interpreting shear influence lines for beams, with and without hinges, using moving unit loads to determine maximum shear and scale by the actual load.

Learn to use moment influence lines to locate vehicle positions that maximize bending moments on beams, and to qualitatively draw influence lines for points like G, B, C, and E.

Explore how a moving unit load shapes truss member forces via influence lines, using DJ and EJ as examples, with tension, compression, and zero-force conditions.

Analyze moving uniformly distributed loads on a truss bridge to determine maximum axial forces in the top chord, bottom chord, and inclined member BC using influence lines.

Apply influence lines to determine maximum reactions, shear, and bending moments in a short-span bridge under permanent deck and girder self-weight and HL-93 transient loads.

Apply the work-energy principle to calculate deflections in beams and trusses using energy methods and the method of joints, with external work and internal energy governed by Hooke's law.

Use the work-energy principle to compute beam and frame deflections by equating external work to internal energy, invoking bending moment and neutral axis concepts.

Apply the virtual work method to a statically determinate truss, equating external and internal virtual work to compute displacements at joints C, B, and D.

Apply the virtual work method to a multi-member frame to compute horizontal displacement and joint rotation, incorporating axial and bending deformations with unit-load and moment analyses.