Fundamentals of Mechanics of materials - FE Civil Exam

Learn how to analyze shear and bending moment diagrams for beams by distinguishing concentrated and distributed loads, computing resultants and reactions, and applying equilibrium to plot accurate diagrams.

Solve a fixed-free beam under two 8 kN loads at 3 m and 6 m; compute vertical reaction, bending moment, and draw shear force and bending moment diagrams.

Solve a second beam example with two downward vertical loads and two supports, determine vertical reactions via moment summation about a point, and draw the shear and bending moment diagrams.

Develop a concise method to derive the bending moment and shear force diagrams for a beam with vertical loads, distributed forces, and supports, using backward calculation from the given data.

Practice exam solution (part 2) guides you through drawing a free body diagram, calculating support reactions, and identifying the maximum shear force in a beam.

Analyze a beam with a triangular distributed load, determine support reactions, locate the resultant via centroid, and compute the bending moment at seven meters for a civil FE exam practice problem.

Explore normal and shear stresses, define bending stresses as an indirect form of normal forces, identify combined stresses, and examine thermal stresses, with examples and problem-solving practice.

Explore normal stress from axial loading, using sigma equals F over A, and see a solved example that finds maximum force via equilibrium of internal and external forces.

Define normal strain as percent change in length under external force; relate stress and strain with Young's modulus; use delta = P L /(A E) and include Poisson's ratio.

Explains bending stress in beams, showing compression at the top fiber and tension at the bottom, with sigma equals M y over I and the neutral axis at the centroid.

This lecture explains shear stress and tau equals v over a, shows nonuniform distribution with center maximum, and presents a 16 kip bolt example with two 8 kip shear planes.

Explore torsion stress in circular shafts, derive tau equal to T r over J, and work through a solved example to find maximum shear stress at the outer radius.

Explain torsion strain and the angle of twist in a shaft, and show a solved example using torque, length, and shear modulus to compute twist in radians and degrees.

Learn torsion in hollow thin-walled circular shafts, distinguish thin and thick sections, and calculate shear flow and area with a 12.5 mm wall and 280 N·m torque.

Learn to distinguish thin-walled and thick-walled cylindrical and spherical pressure vessels and analyze hoop, axial, and radial stresses with solved examples to determine minimum wall thickness.

Explore thermal expansion and the resulting stress in materials using alpha and delta t, where epsilon equals alpha delta t and stress equals E times epsilon, shown in solved example.

Demonstrates how to determine normal force distribution and compute stress in bar segments with varying axial loads, using a normal force diagram and calculating sigma1, sigma2, and sigma3.

Examine how to compute axial and transverse strains in a steel plate under 30 MPa using E = 200 GPa, update dimensions, and use answer-elimination strategies to save time.

analyze an aluminum-bronze bar under torsion, noting that torsion stress depends on radius and the polar moment of inertia, not on material; the solution says aluminum torsion differs from bronze.

Practice exam solution demonstrates calculating torsion on a shaft from a lateral force, determining shear stress, and the maximum angle of twist using G and aluminum shaft geometry.

Explore the practice exam solution (part 5) as a simple quiz question narrowed to a range 0 to 0.5, illustrating time-efficient strategies for the FE civil exam.

Compute the tensile stress in a thin-walled steel cylinder under 850 kPa, with 0.175 m radius and 6 mm wall, yielding about 24.8 MPa.

Calculate elongation by equating stress to yield, compute strain with E = 69 GPa for 2.5 m length, yielding about 9.25 mm of elongation.

Calculate principal stresses by rotating the stress element and using sigma1,2 = (sigma_x+sigma_y)/2 ± sqrt(((sigma_x-sigma_y)/2)^2 + tau_xy^2), with example sigma_x=50, sigma_y=-10, tau_xy=40, yielding 70 and -30.

Calculate strains from combined stresses in three dimensions using general strain equations, understand sign conventions, and apply a worked example to determine epsilon_y.

Explore Mohr circle as a graphical method to determine normal and shear stresses for different orientations without transformation equations, identify principal stresses, and understand the radius equals maximum shear stress.

Solves the first practice exam problem by calculating principal stresses from sigma_x, sigma_y, and tau_xy using the standard formula, yielding 270 MPa and -330 MPa.

Apply the principal-stress calculation to a stress element by using sigma_x and sigma_y to compute sigma1 and sigma2, yielding 92.5 and -8.5.

Apply the provided stress transformation formula to the given sigma_x, sigma_y, and tau_xy in the quiz problem, yielding a maximum stress of 199.3 MPa.

Conclude the fundamentals of mechanics of materials and prepare for the next topic by reviewing examples to refresh memory, and join the private Facebook group for clarifications.