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.

Assess stability and determinacy of structures using free-body diagrams for beams and frames with fixed, rocker, and collar or pin supports.

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 simply supported beams under loads by replacing each load with an equivalent concentrated load at its centroid and solving for support reactions; covers uniform, triangular, trapezoidal, and nonlinear loads.

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.

Identify zero-force members in statically determinate trusses using qualitative joint analysis, rotating coordinate axes to reveal zero forces and simplify the structure.

Identify zero-force members in trusses through an interactive online quiz. Test your structural engineering knowledge and sharpen analytical skills as you explore bridges, roofs, domes, and towers.

Use the method of sections to calculate a specific member force in a statically determinate truss. Cut through selected members, draw a free-body diagram, and solve equilibrium equations for the target force.

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.

Master the method of sections for truss analysis and learn why isolating a joint with three or more unknowns fails; use a substructure to obtain distinct equations determining member forces.

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.

Use the method of joints to analyze a statically determinate floor truss, converting a 3 kN/m distributed load into joint loads through four floor slabs.

Use the method of joints to solve a statically determinate seven-member truss, calculating support reactions and joint equilibria to determine each member force and tension or compression.

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.

Learn to derive shear and bending moment equations for beams under rectangular, triangular, trapezoidal, and nonlinear distributed loads, using free-body diagrams and equilibrium.

Derive piecewise shear and moment functions for a statically determinate beam by applying free-body diagrams, equilibrium, and sign conventions, yielding V(x) and M(x) for left and right segments.

Derive shear force and bending moment equations for a statically determinate beam, using left and right segments and cut points to reveal internal V(x) and M(x) with piecewise definitions.

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.

Construct shear and moment diagrams for a simply supported beam under a mixed rectangular-triangular load without equations, using areas under load to locate the zero-shear point and peak bending moment.

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.

Learn to construct shear and moment diagrams for a simply supported beam without writing equations, using support reactions and the area under the load diagram.

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.

Explore how beams deflect under loads by drawing the elastic curve, analyzing supports and rotations, and using bending moment diagrams to relate moments to the deflected shape.

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.

Use the double integration method to derive deflection equations for a two-segment beam with E_a and E_s, enforcing continuity at the junction and boundary conditions to obtain the elastic curve.

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.

Apply the moment-area method to find slope and deflection in beams using the area under the M/EI diagram; learn first and second moment-area theorems through cantilever and simply supported scenarios.

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.

Apply truss influence lines to a moving three-axle truck load on a deck-supported bridge to determine the maximum axial compressive and tensile forces in a truss member.

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.

Construct floor girder influence lines under moving floor loads using unit loads at transfer points and superposition to derive shear and bending moment patterns.

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 calculate beam deflection at the midpoint and rotation by equating external and internal virtual work, using a virtual unit load and bending moment equations.

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.