Engineering Mechanics- College Level- Statics Part II

Explore self weight as an evenly distributed force and apply it to cantilever beams, calculating support reactions by lumping distributed loads, using moments and center of gravity concepts.

Explore fixed supports in cantilever beams by enforcing three conditions: zero x-forces, zero net y-forces, and zero moments. Learn to compute rax, ray, and maz with a self-weight example.

Solve cantilever beam problems with distributed and concentrated loads by drawing a free body diagram and calculating horizontal and vertical reactions and moments, including R_Ax, R_Ay, and M_Az.

Explore triangular non-uniform loads and how to compute lumped forces, their location via centroids in beams, and extend to arbitrary force distributions using area under the curve.

Analyze a triangular distributed load of 60 lb/ft on a 9 ft beam to determine support reactions and moment using free-body diagrams and force and moment equations.

Explore moments and force couples in statics, showing how equal and opposite forces create rotation and are represented by a moment M that affects the moment equation, not force equilibrium.

Compute the support reactions and end moment for a cantilever beam subjected to a four-meter uniform load and two 100 kN·m concentrated moments, using force and moment equilibrium.

Learn to model structures with evenly distributed and concentrated forces, determine fixed-support reactions, and apply equilibrium with moments on cantilever beams in two dimensions.

Explore structural stability and the distinction between statically determinant and externally aesthetically indeterminate systems, and learn to identify and calculate support reactions for statically determinant component systems.

Explore stability of two-dimensional structures by examining how different support configurations affect static equilibrium, determinacy, and aesthetics, and why extra supports can over-stabilize or render systems kinetically unstable.

Identify the three statically determinant base systems—simply supported beam, cantilever beam, and hinged simply supported frame—and explain how hinges provide boundary conditions to stabilize and form complex structures.

Explore hinges in statics, showing how rotation is allowed and the moment at the hinge is zero, clarifying the distinction between sum of moments and the hinge moment.

Explore statically determinate compound systems using hinges and moment boundary conditions. Solve for support reactions by forming subsystems and applying equilibrium, as in cantilevers, simply supported frames, and overhang beams.

Explore how many times a system is aesthetically indeterminate, why three equations may be insufficient, and distinguish external versus internal indeterminacy from boundary conditions and connections.

Explore analysis of simple and compound statically determined beams using free body diagrams and moment equations. Understand symmetry, hinges, and multiple support reactions in complex structures.

Identify statically determinate systems and distinguish determinant from indeterminate cases, using hinge boundary conditions to calculate support reactions. Apply this to four homework problems on simple and compound beam systems.

Explore internal forces in rigid bodies, starting with 3D to 2D understanding, including shear forces, normal forces, and bending moments, through the reference fiber and equilibrium concepts for beams.

internal forces include normal forces, shear forces, and bending moments; normal forces indicate tension or compression, shear forces act parallel to the cut surface, and bending moments act about z-axis.

Determine support reactions, cut at the point of interest, draw the free-body diagram, and apply the three equilibrium equations to find m(c), v(c), n(c).

Explore the internal forces sign convention using the reference fiber to define positive normal, shear, and moment directions, with left and right cuts and X as the position variable.

Explore how to compute internal forces—normal force, shear, and bending moment—along a simply supported beam under concentrated loads using free-body diagrams and cuts.

Identify how rigid bodies are held together by internal forces and released as forces via virtual cuts. Apply free body diagrams and equilibrium to determine internal forces and support reactions.

Explore graphing internal forces and bending moments by introducing concentrated force diagrams, defining domains, and preparing to extend to distributed loads in subsequent lessons.

Explore graphing internal forces and bending moments on a beam by using prior support reactions and point values to create three graphs for normal force, shear force, and bending moment.

Identify the normal force diagram in newtons, noting negative values indicate compression and using a reference fiber for x y coordinates. Apply equilibrium and relate the horizontal component.

Draw and interpret a shear force diagram by tracing constant segments, jumps, and zero starting points, clearly identifying positive and negative regions using newton units.

Draw and interpret the bending moment diagram for a system with concentrated forces, noting the moment values, lever arm effects, slope changes, and zero moments at hinges.

Explore the relationship between the shear force diagram and the moment diagram: shear force is the derivative of the moment, while the moment mirrors the integral of shear force, with positive bending.

Explore internal force analysis in a statics problem, calculating reactions, cuts, and diagrams for normal force, shear force, and bending moment at locations B and C.

Learn to locate and graph internal forces along a beam for concentrated loads, including normal force, shear force, and moment, with proper diagrams, units, and sign conventions.

Explore how evenly and unevenly distributed forces shape internal force diagrams, and learn to describe internal forces at finite points along a beam, setting up for infinitesimal analysis.

Explore how self weight and distributed forces shape force diagrams, where a distributed load yields a linear shear force and a parabolic moment, with shear force as the moment’s derivative.

Explore how not evenly distributed loads create a linear slope, producing a parabolic shear force and cubic moment, with integration revealing deflection and safety implications.

Apply a tool that links load cases to shear force and bending moment diagrams. Understand jumps, inflection points, and parabolic or cubic moments from concentrated loads, moments, and distributed loads.

Learn to draw internal force diagrams in statics by making cuts, applying symmetric support reactions (2000 lb each), and deriving shear, moment, and normal force diagrams for distributed loads.

learn to determine internal forces and bending moments for distributed loads, relate shear force and bending moment diagrams through differential analysis, and practice drawing these diagrams from homework problems.

Derive the shear force function V(x) from internal force diagrams along a beam, then extend to bending moments and graph the resulting internal functions.

Derive the shear force as a function of x for a beam with a left support and right cut under evenly distributed and triangular loads, using base and height.

Develop and apply bending moment functions M(x) for evenly distributed and triangular loads, using lever arms x/2 and x/3, revealing quadratic and cubic dependencies and domain considerations.

Develop and verify the shear force and moment functions for multi-domain beams, compute support reactions, identify zero shear locations, and sketch the shear force and bending moment diagrams.

Develop shear force and bending moment functions, and explain why load cases shape them. Practice deriving internal force functions and the maximum moment m_max = w l^2/8 for distributed loads.

Explore internal forces in hinged beams, where the moment is zero at the hinge, and see how this shapes internal force diagrams for a simply supported hinge beam.

Hinges transmit all internal forces except the moment, which is zero at the hinge; shear and normal forces remain, and we briefly discuss other connection types.

Explore how a hinge governs internal forces by forcing the moment diagram to pass through zero at the hinge, and note that constant loads yield linear shear and parabolic moments.

Explore example problems on statics: analyze beams with hinges, simply supported and cantilever sections, compute reactions, and construct normal, shear, and moment diagrams under distributed and concentrated loads.

Review how hinges affect internal forces and moments in simply supported hinged structures, noting zero moment at the hinge and unchanged normal and shear diagrams.

Explore orthogonal hinged frames by examining rectangular corners and implementing hinges in frames, then derive internal force diagrams for rectangular frames.

Analyze internal forces at a 90-degree corner by cutting a frame, showing how moment, shear, and normal forces balance and interact with the reference fiber.

Learn to analyze hinged frames by identifying four essential support reactions, using two independent moment equations about chosen cuts to solve for rb x and rb y.

Learn to construct free-body diagrams and internal force diagrams for a hinged frame, determine support reactions, and analyze moments, shear forces, and normal forces under distributed and concentrated loads.

Master determining support reactions and internal force diagrams for orthogonal frames, using reference fibers and sign conventions, while solving six homework problems to prepare for non-orthogonal frames and roof structures.

Explore internal forces in non orthogonal hinged frames, such as roof structures with angled corners, and draw force diagrams for self weight, snow load, wind load, and their support reactions.

Analyze self-weight on a hinged non-rectangular roof frame: compute symmetric support reactions for a 500 N/m load, decompose into parallel and perpendicular components, and derive normal, shear, and moment diagrams.

Explore how snow load is a projected, geography-based force on rafters, converted to per-length values and decomposed into parallel and perpendicular components to determine reactions and moments.

Explore wind loads in statics, distinguishing windward and leeward sides, with forces perpendicular to the beam, and learn to compute support reactions and draw shear and moment diagrams.

master how to identify self weight, snow and wind load cases, compute vertical and horizontal support reactions, decompose forces, and sketch roof-structure internal force diagrams for homework A and B.