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Learn MoreMechanics of Materials Made Easy: Ace Your Engineering Exams
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Mechanics of Materials Made Easy: Ace Your Engineering Exams
A Comprehensive Guide to Statics, Stress Analysis, and Structural Design for Engineering Students and Professionals.
Created byRateeb Yehya, M.S., P.E.
Last updated 12/2024
English
English [Auto],
What you'll learn
- Understand Fundamental Concepts of Mechanics of Materials
- Analyze Structural Components Under Various Loading Conditions
- Apply Problem-Solving Techniques in Real-World Scenarios
- Design Safe and Efficient Structural Elements
- Master Stress Transformation Techniques
- Evaluate Material Properties and Their Impact on Structural Behavior
- Calculate Axial, Shear, and Bending Deformations
- Analyze and Design Composite Beams and Eccentric Load Scenarios
- Understand the Effects of Temperature on Structural Elements
- Apply Compatibility Equations to Indeterminate Structures
- Understand Torsional Effects in Circular Sections
- Utilize Combined Loading Analysis
- Assess Structural Safety with Allowable Stress Design
- Prepare for Advanced Engineering Studies or Professional Exams
Explore related topics
Course content
10 sections • 179 lectures • 42h 39m total length
- Types of Supports, Loads, and Beams.16:37
This lecture introduces the fundamental types of supports (fixed, pinned, roller), common load types (point loads, distributed loads, moments), and standard beam configurations used in mechanics of materials. Essential for understanding structural analysis and support reaction
- Continued11:34
This lecture is a continuation of the previous lecture.
- The Three Equilibrium Equations in 2-D Statics Problems11:41
Learn how to apply the three fundamental equilibrium equations—∑Fx = 0, ∑Fy = 0, and ∑M = 0—in two-dimensional statics problems. This lecture includes clear examples and strategies for solving support reactions and internal forces.
- Internal Forces16:37
This lecture explains internal forces in beams and structural members, including normal force, shear force, and bending moment. Learn how to identify and analyze these forces through methodical section cuts and equilibrium.
- Problem 121:02
- Problem 1 Continued9:31
- Problem 219:05
Analyze a simply supported beam with triangular loads, compute reactions at A and D by equilibrium, and determine internal reactions at A, B, and C using resultant forces.
- Problem 320:16
Divide the beam at the hinge to form two parts, apply moment sums to find reactions at supports, then derive shear and bending diagrams for points like D and B.
- Method of Equations22:44
This lecture explains the Method of Equations used to analyze statically determinate structures. We set up and solve equilibrium equations to determine unknown reactions and internal forces in beams and frames.
- Problem 429:36
Apply the method of equations and the method of sections to determine reactions, internal forces, and bending moments for a fixed beam with triangular loading and a moment.
- Method of Integration (Area Method)17:49
In this lecture, we introduce the Method of Integration, also known as the Area Method, for calculating deflection and slope in beams. We explain how to integrate the moment-curvature relationship and apply boundary conditions to solve for beam deformation.
- Continued22:35
- Problem 512:38
Use the area method or graphical method to draw shear and bending moment diagrams, account for jumps from concentrated forces and moments, and ensure they close to zero.
- Problem 621:00
Learn to draw shear and bending moment diagrams for an overhanging beam with triangular and rectangular loads using graphical integration method, including calculating reactions and area techniques for second-degree curves.
- Problem 714:25
- Definition and Types of Stresses13:35
Understand what stress means in mechanics of materials and explore its main types: normal stress, shear stress, and bearing stress. This lecture builds the foundation for analyzing how materials respond to external loads.
- Units of Stresses11:52
Learn the common units used to measure stress in materials, including psi, pascals, and megapascals. Understand unit conversions and their importance in engineering calculations.
- Average Normal Stresses9:07
This lecture covers the concept of average normal stress, how it is calculated by dividing axial force by cross-sectional area, and its significance in assessing material performance under load.
- Mode of Failure Under Normal Stresses13:07
Discover the common failure modes materials experience under normal (axial) stress, such as tensile rupture, compressive crushing, and buckling. This lecture explains how and why these failures occur in structural elements.
- Problem 1 - Normal Stresses17:57
- Problem 2 - Normal Stresses8:55
Explore normal stresses in a cantilever under a uniformly distributed axial load, determine the internal normal force at section A, then compute average stress using the cross-sectional area.
- Problem 3 - Normal Stresses8:51
- Problem 4 - Normal Stresses15:55
- Problem 5 - Normal Stresses11:22
learn to compute average normal (compressive) stress on a plane in a steel cylinder by using specific weight gamma, volume, and cross-section area, via weight over area.
- Problem 6 - Normal Stresses9:30
Apply equilibrium and moment equation to a beam with normal stresses, draw a free body diagram, and find x so that sigma_ab equals sigma_c, using areas 400 and 650 mm^2.
- Average Shear Stresses11:23
Learn how to calculate average shear stress by dividing shear force by the cross-sectional area. This lecture covers its significance in evaluating material behavior under shear loading conditions.
- Example of Average Shear Stresses12:09
This lecture explains the Method of Equations used to analyze statically determinate structures. We set up and solve equilibrium equations to determine unknown reactions and internal forces in beams and frames.
- Problem 7: Average Shear Stresses14:24
- Mode of Failure Under Shear Stresses12:48
Explore the typical failure modes caused by shear stresses, including shear fracture, sliding failure, and material yielding. Understand how materials respond and fail when subjected to shear forces.
- Problem 8 - Average Shear Stresses11:56
Learn to determine the largest internal shear force in a bolt connecting five plates by drawing free body diagrams, applying equilibrium, and analyzing the bolted assembly.
- Problem 9 - Average Shear Stresses10:27
- Problem 10 - Average Shear Stresses8:38
Determine the average shear stress on planes AA and BB by drawing a free body diagram, using a 3 kN force and areas 100×150 mm and 125×150 mm.
- Problem 11 - Average Shear Stresses15:59
- Bearing Stresses - Definition and Types13:26
This lecture defines bearing stress and explores its types, focusing on how contact pressures develop between two surfaces. Learn why bearing stress is critical in design to prevent surface crushing or deformation.
- Mode of Failure Under Bearing Stresses9:02
Understand how materials fail under bearing stresses, including surface crushing, indentation, and localized deformation. This lecture explains common failure patterns and design considerations to prevent bearing failure.
- Problem 12 - Bearing Stresses16:42
- Problem 13 - Bearing Stresses15:48
Determine bolt diameter and washer outer diameter for a compound wooden beam by computing the force at B via a free-body diagram and applying allowable tensile and bearing stresses.
- Problem 14 - Bearing Stresses11:40
- Extra Exercises - Problem 1514:15
Determine the maximum chandelier mass by analyzing average stresses in two rods and applying a free body diagram and equilibrium with theta 45 degrees.
- Extra Exercises - Problem 1610:25
- Extra Exercises - Problem 1713:00
- Allowable Stress Design14:23
Learn the principles of Allowable Stress Design (ASD), where structures are designed to keep stresses within safe limits under service loads by applying safety factors. This lecture explains its applications and advantages in structural engineering.
- Problem 18 - Allowable Stress Design9:45
- Problem 19 - Allowable Stress Design13:18
Determine the maximum allowable force by applying the factor of safety to spar compressive stress, pin shear, and bearing stresses in double shear, yielding 47,124 N.
- Problem 20 - Allowable Stress Design14:23
- Axial Deformations10:02
This lecture covers axial deformation of structural members under tension or compression. Learn how to calculate elongation or shortening using stress, strain, and material properties like Young’s modulus.
- Shear Deformations10:50
Understand how materials deform under shear forces. This lecture explains shear strain, shear modulus, and how to calculate shear deformation in beams and structural members.
- Shear Strain and Normal Strain11:24
Learn the difference between shear strain and normal strain, how each represents deformation in materials, and their roles in analyzing stresses and displacements in structures.
- Problem 1 - Average Normal Strain11:21
Learn to solve a rigid beam problem by calculating average normal strain in wires H, CG, and FD using deformed shapes and tangent geometry.
- Problem 2: Average Normal Strain10:17
Analyze average normal strains in two fixed wires AC and AB under a 2 mm displacement at A using deformed shapes to compute final lengths and thus epsilon_AC and epsilon_AB.
- Problem 3: Average Normal Strain9:25
Compute point d displacement using the average normal strain in AB, determine AB's initial length via Pythagoras, then use similar triangles to link delta d and delta b.
- Problem 4: Average Normal Strain10:11
Calculate the average normal strains along ad and db from the deformed rubber using geometric deformation and Hooke's law; ad elongates slightly, while db contracts.
- Problem 5: Average Normal Strain6:37
Compute displacement under nonuniform loading by integrating the normal strain epsilon(x)=k x^2 along the beam, yielding delta at a point (k L^3/3) and the average normal strain k L^2/3.
- Problem 6: Average Normal Strain7:34
Set perpendicular axes at undeformed point and measure theta between x and y', then gamma = pi/2 − theta, alpha ≈ 0.286° and beta ≈ 0.764°, gamma ≈ −0.0082 rad.
- Law Of Cosines5:20
This lecture explains the Law of Cosines, a fundamental trigonometric formula used to find unknown sides or angles in any triangle. Learn its derivation and applications in solving statics and mechanics problems.
- Problem 7: Average Shear Strain12:18
- Continued9:03
Apply the cosine law on triangle db prime cb prime to find e prime b prime, then compute theta and convert to radians to determine the strain.
- Strength and Ductility11:49
Explore the concepts of strength and ductility in materials, understanding how materials resist failure and deform plastically before breaking. Learn why these properties are crucial for safe and reliable structural design.
- Toughness and Stiffness7:13
This lecture covers the concepts of toughness and stiffness in materials. Learn how toughness measures a material’s ability to absorb energy before failure, while stiffness relates to its resistance to deformation under load.
- Tension Test13:18
Discover how the tension test is used to determine the mechanical properties of materials, including tensile strength, yield strength, and elongation. This lecture covers the test setup, procedure, and interpretation of results.
- Normal Stress Strain Diagram and Hooke's Law11:52
This lecture explains the normal stress-strain relationship in materials and introduces Hooke’s Law. Learn how elastic deformation follows a linear pattern and how to calculate stress and strain in structural members.
- Inelastic Phase - Part 112:53
This lecture explores the inelastic phase of material behavior, where permanent deformation occurs beyond the elastic limit. Understand yield strength, plastic deformation, and the difference between elastic and plastic regions in stress-strain curves.
- Inelastic Phase - Part 212:52
Explore how the stress–strain diagram defines stiffness, strength, ductility, toughness, and resilience, detailing modulus of elasticity, ultimate stress, and energy absorption for elastic design against earthquakes.
- Load Removal - Elastic Phase12:40
This lecture discusses the behavior of materials during load removal within the elastic phase. Learn how materials return to their original shape without permanent deformation, illustrating elastic recovery and energy conservation.
- Load Removal - Inelastic Phase11:08
This lecture explains what happens when a load is removed during the inelastic phase of a material. Learn about permanent deformation, hysteresis, and the differences between elastic recovery and plastic strain.
- Problem 1 - Normal Stress Strain Diagram12:33
- Continued11:02
- Shear Stress Strain Diagram11:57
This lecture covers the shear stress-strain relationship in materials. Learn how shear forces cause deformation, how to interpret the shear stress-strain diagram, and the material behavior under shear loading.
- Problem 2: Shear Stress Strain Diagram8:29
Apply shear stress concepts to solve a problem on a plastic sheet: compute the force P for a 0.8 inch displacement using gamma, tau, and Hooke's law under elastic behavior.
- Problem 3: Average Shear Strain10:17
Learn to analyze average shear strain in a two-pad rubber assembly by applying double shear concepts, using free-body diagrams, gamma geometry, and Hooke's law to link force, area, and displacement.
- Poisson's Ratio10:57
This lecture explains Poisson’s Ratio, the measure of the lateral strain to axial strain in materials under load. Understand how this ratio affects material deformation and its importance in stress analysis.
- Problem 4: Poisson's Ratio10:48
Apply Poisson's ratio to an axial load on an A36 steel bar, using modulus of elasticity and Hooke's law to compute longitudinal and lateral strains, deformations, and volume change.
- General State of Stress13:38
This lecture introduces the concept of the general state of stress at a point in a material, covering normal and shear stress components acting on different planes. Learn how to represent and analyze multi-axial stress conditions in solids.
- Example on the General State of Stress5:32
Explain the general state of stress by setting axes, determine signed stresses in x, y, z for compression and tension, and apply the formulas to find epsilon.
- Problem 5: General State of Stress7:27
The session guides solving a plane stress problem by deriving sigma_x, sigma_y, and epsilon_z from epsilon_x and epsilon_y, using the general state of stress, identifying axes and signs.
- Problem 6: General State of Stress10:17
- Problem 7: General State of Stress13:09
Analyze the general state of stress with no slipping, set epsilon_x and epsilon_y to zero, relate sigma_x and sigma_y to sigma_z via Poisson's ratio and E, compute delta_z.
- Continued6:24
By expressing sigma x and sigma y in terms of sigma z, this lecture derives epsilon z and simplifies it to (1/E) sigma z (1+mu)(1-2mu)/(1-mu), showing contraction.
- Problem 8: General State of Stress13:08
Apply Hooke's law to find axial stress and deformation of a 60 kN steel bar from the stress–strain diagram, then use Poisson's ratio to estimate diameter and volume change.
- Continued10:19
Learn to compute permanent deformation after load removal under axial loading by tracing a line parallel to the elastic slope on the stress-strain diagram to determine permanent strain.
- Problem 9: General State of Stress12:28
Explore the general state of stress and bulk modulus through a brass cylinder under axial and hydrostatic loading, deriving strain, volumetric strain, and bulk modulus from given properties.
- Dilation and Bulk Modulus10:05
This lecture covers dilation, the volumetric strain response of materials under pressure, and bulk modulus, which quantifies a material’s resistance to uniform compression. Understand how these concepts apply to fluid and solid mechanics.
- Axial Deformation: General Formula15:49
This lecture derives the general formula for axial deformation in structural members under axial loads. Learn how to calculate elongation or compression using stress, strain, and material properties like Young’s modulus.
- Axial Deformation: Sudden Changes in Internal Force10:45
This lecture explores axial deformation in members and how sudden changes in internal forces—such as at load application points or supports—affect deformation. We discuss how to calculate elongation or compression in axially loaded elements.
- Axial Deformation: Sudden Changes in Area6:49
This lecture discusses how sudden changes in cross-sectional area affect axial deformation and stress distribution in structural members. Learn to analyze stress concentration and its impact on material performance.
- Axial Deformation: Sudden Changes in Modulus of Elasticity5:08
This lecture examines how abrupt changes in the modulus of elasticity within a structural member influence axial deformation. Understand how material property variations affect stress and strain distribution under axial loads.
- Axial Deformation: Continuous Change in Load12:53
This lecture covers axial deformation in members subjected to continuously varying axial loads. Learn methods to calculate elongation and stress when load intensity changes gradually along the length.
- Axial Deformation: Continuous Change in Area15:59
This lecture explores axial deformation in members where the cross-sectional area changes gradually along the length. Learn how to analyze stress and strain distributions using calculus-based methods.
- Axial Deformation: Temperature Effects13:21
This lecture explains how temperature changes cause axial deformation in structural members. Learn about thermal expansion, contraction, and how to calculate stresses induced by temperature variations.
- Example on Temperature Effects9:51
- Indeterminate Structures10:42
This lecture introduces indeterminate structures—systems with more unknown forces than equilibrium equations. Learn methods such as compatibility equations and superposition to analyze these complex structures.
- Compatibility Equation Form 19:01
This lecture explains the first form of the compatibility equation used in structural analysis to relate deformations and ensure continuity in indeterminate structures. Learn how to set up and solve these equations to find unknown forces and displacements.
- Problem 1: Compatibility Equation16:09
This lecture introduces compatibility equation for an indeterminate fixed-bar structure with prismatic segments, guiding you through segment cuts, unknown reactions, and delta total equals zero to find reactions.
- Continued5:58
Calculate delta AB, delta BC, and delta CD as delta force plus delta temperature, with force = N L/(A E); N_BC = R_A - 25.5, N_CD = R_A - 8.5.
- Problem 2: Compatibility Equation14:40
Explore compatibility equations for indeterminate composite bars, solving for aluminum and steel stresses by balancing delta force and delta temperature in a two-segment model with unyielding supports.
- Compatibility Equation Form 28:24
This lecture covers the second form of the compatibility equation used in analyzing indeterminate structures. Learn how to apply deformation compatibility conditions to solve for redundant forces and ensure structural continuity.
- Problem 3: Compatibility Equation18:17
Solve a two-rod indeterminate problem with a 0.5 mm gap and a 120° temperature rise, using the form two compatibility equation to determine end reactions and aluminum stress.
- Compatibility Equation Form 39:13
This lecture presents the third form of the compatibility equation used in structural analysis of indeterminate systems. Learn how to relate deformations and apply boundary conditions to solve for unknown redundant and ensure structural equilibrium.
- Problem 4: Compatibility Equation14:21
Explore indeterminate columns by distributing a 10 kN compression between concrete and six 22 mm steel bars under 35°C rise, using the compatibility equation delta steel equals delta concrete.
- Continued7:12
- Compatibility Equation Form 47:47
This lecture explains the fourth form of the compatibility equation for indeterminate structures. Learn advanced techniques to relate deformations, apply boundary conditions, and solve complex structural problems with one redundant.
- Problem 5: Compatibility Equation22:15
Solve a fourth form compatibility problem for a rigid beam with two cables using Thales theorem, incorporating temperature rise and factor of safety to find the allowable load.
- Compatibility Equation Form 519:59
This lecture covers the fifth form of the compatibility equation in structural analysis. Learn how to apply deformation compatibility and equilibrium conditions to solve complex indeterminate structures with multiple redundants.
- Normal Stresses Due to Bending17:51
This lecture explains how bending moments create normal stresses in beams. Learn how to calculate bending stress distribution using the flexure formula and understand the concept of the neutral axis.
- Linear Variation of Normal Stresses and the Neutral Axis13:31
This lecture covers the concept of linear variation of normal stresses across a beam’s cross section due to bending. Learn about the neutral axis—the line of zero stress—and how stress varies linearly from compression to tension zones.
- Locating the Neutral Axis for Single Bending13:47
This lecture explains how to locate the neutral axis in beams subjected to single bending. Learn the method to find the axis where bending stress is zero and how it influences the stress distribution across the cross section.
- Locating the Centroid of a Cross Section14:42
This lecture teaches how to find the centroid (center of mass) of various cross-sectional shapes. Understanding the centroid location is essential for analyzing bending stresses and designing structural members.
- Problem 1: Locating the Centroid10:00
Identify the coordinate system and axis of symmetry to locate the centroid of a beam cross-section, then apply the composite area method with A1, A2, y1_bar, y2_bar.
- Problem 2: Locating the Centroid9:17
Identify the coordinate system, partition the cross section into rectangles, compute areas and centroids from a bottom reference, and locate y-bar and x-bar to determine the neutral axis.
- Problem 3: Locating the Centroid11:56
Learn to locate the centroid of a non-symmetric beam cross section by partitioning into simple shapes, calculating x-bar and y-bar from area moments, and recognizing symmetry in I-beams.
- Moment of Inertia16:35
This lecture introduces the concept of the moment of inertia for beam cross sections, explaining its role in resisting bending. Learn how to calculate moments of inertia for common shapes and their importance in structural analysis.
- Problem 4: Moment of Inertia14:21
- Problem 5: Moment of Inertia11:35
Locate the centroidal axes of the beam cross-section, then partition into rectangles and apply the parallel axis theorem to compute Ix and Iy.
- Problem 6: Moment of Inertia13:08
- Pure Bending About a Horizontal Axis14:28
This lecture explores pure bending in beams about a horizontal axis, where bending moment is constant along the length. Learn how stresses and strains develop under pure bending and the assumptions behind the bending theory.
- Problem 7: Pure Bending About a Horizontal Axis14:10
Calculate maximum tensile and compressive stresses from pure bending about a horizontal axis by using Mx, y, and Ix with neutral axis and bending moment diagrams.
- Problem 8: Pure Bending About a Horizontal Axis15:46
Compute reactions, draw shear and bending moment diagrams, and determine maximum tensile and compressive stresses for pure bending about the z axis in an I-beam using I_z.
- Continued11:53
- Problem 9: Pure Bending About a Horizontal Axis12:02
Compute tensile and compressive stresses from bending by constructing shear and bending moment diagrams for a u-shaped beam, and determine neutral axis, moment of inertia, and stress at point e.
- Continued13:48
Continue by analyzing cross-sectional properties, locating the neutral axis and centroid, and calculating the moment of inertia, then analyze two bending cases to obtain maximum compressive and tensile stresses.
- Problem 10: Pure Bending About a Horizontal Axis19:41
Apply the method of equations to derive shear and bending moment expressions for a cantilever with hollow cross sections, using two cuts (x1, x2) to plot the diagrams.
- Continued7:39
Calculate cross-sectional properties for a symmetric hollow section, locate the neutral axis at mid-height, and determine the maximum compressive (top fiber) and tensile (bottom fiber) stresses in pure bending.
- Pure Bending About a Vertical Axis13:22
This lecture covers pure bending of beams about a vertical axis. Learn how bending moments create stress distributions in this orientation and how it differs from horizontal axis bending.
- Problem 11: Pure Bending About a Vertical Axis9:38
Learn to solve pure bending about a vertical axis, locate the neutral axis, and determine maximum compressive and tensile stresses under a 150 kilonewton meter moment.
- Locating the Neutral Axis in Double Pending20:35
This lecture explains how to locate the neutral axis in beams subjected to double bending moments about two axes. Learn techniques to analyze complex stress distributions and understand the combined effects of bending in multiple directions.
- Problem 12: Locating the Neutral Axis in Double Bending14:52
Under mechanics of materials, locate the neutral axis and compute corner stresses for a rectangular section under a two-axis bending moment, using moment projections and the right-hand rule.
- Continued17:47
Learn to analyze double bending by locating centroidal axes and computing I z and I y. Use the right-hand rule to project moments and assess tensile and compressive stresses.
- Problem 13: Locating the Neutral Axis in Double Bending18:09
This double-bending lecture demonstrates locating the neutral axis by projecting the moment vector, applying the right-hand rule for compression zones, and computing centroidal properties to obtain compressive and tensile stresses.
- Continued7:14
- Eccentric Loads (Part 1)16:12
This lecture explains how eccentric loads—loads applied away from the centroid—create combined axial and bending stresses in structural members. Learn to analyze the resulting stress distribution and calculate moments caused by eccentricity.
- Eccentric Loads (Part 2)21:17
- Problem 14: Eccentric Loads18:36
- Composite Beams21:51
This lecture covers composite beams made of two or more different materials or sections joined together. Learn how to analyze their combined behavior, calculate equivalent properties, and understand how materials share loads.
- Problem 15: Composite Beams23:40
Explore composite beams of steel and wood, learn to transform via transformation factors to a single material, and compute maximum bending stresses using shear and moment diagrams.
- Problem 16: Composite Beams26:40
transform composite beams to a unified section, compute reactions, shear, and bending moments for a cantilever under uniform load, and determine allowable load by steel and wood bending stresses.
- Composite Beams in Circular Cross Sections14:23
This lecture explores composite beams with circular cross sections made from different materials. Learn how to calculate the combined moment of inertia, analyze stress distribution, and understand load sharing in circular composite members.
- Vertical Shear Stresses (Part 1)25:29
This lecture explains how vertical shear stresses develop in beams subjected to transverse loads. Learn to calculate shear stress distribution across different cross sections and understand its impact on beam design and safety.
- Vertical Shear Stresses (Part 2)25:36
- Problem 1 - Vertical Shear Stresses16:35
- Continued21:08
Determine centroid of a composite cross-section, evaluate q over t at points on the neutral axis and discontinuities, and locate maximum shear stress at smallest thickness, directed by the force.
- Problem 2 - Vertical Shear Stresses25:04
Calculate the maximum vertical shear stress for the beam by building the shear force diagram, locating tau max and its direction, and deriving it from cross-sectional properties.
- Horizontal Shear Stresses21:05
This lecture covers horizontal shear stresses in beams and structural members. Learn how these stresses arise, how to calculate their distribution, and their significance in beam and connection design.
- Problem 3 - Horizontal Shear Stresses27:09
Compute horizontal shear stresses in a composite cross-section. Determine reactions, draw the shear force diagram, and evaluate q over t and tau max via area prime centroids and the moment of inertia.
- Shear Flow23:31
This lecture introduces the concept of shear flow in beams and thin-walled structures. Learn how to calculate shear flow to analyze the distribution of shear forces along flanges and webs, crucial for designing built-up and composite sections.
- Problem 4 - Shear Flow15:38
Determine maximum vertical shear for a seven-board nailed beam using tau max = VQ/(Ix t), compute Ix and Q, and note that maximum shear occurs at the neutral axis.
- Continued16:17
Apply the shear-flow formula to compute s' for nails A and s for nails B in a multi-nail cross-section; s' ≈ 1.69 mm, s ≈ 0.35 mm.
- Problem 5 - Shear Flow34:02
- Torsional Stress14:26
This lecture covers torsional stresses developed in shafts and structural members subjected to twisting moments. Learn how to calculate shear stresses due to torque and understand the effects of torsion on material behavior and design.
- Problem 1 - Torsion13:57
Analyze a hollow pipe under torsion to compute inner and outer wall shear stresses using tau = VQ/It plus tau = T rho/J, with J = 2I.
- Problem 2 - Torsion15:33
Identify the absolute maximum shear stress in a torsioned solid shaft by locating the maximum internal torque with cuts, ensure equilibrium, and apply tau = T rho / J.
- Problem 3 - Torsion9:15
- Angle of Twist13:05
This lecture explains the concept of angle of twist in shafts subjected to torsion. Learn how to calculate the angular deformation along the length of a shaft and understand its impact on mechanical performance.
- Problem 4 - Angle of Twist16:26
- Gears in Mesh14:38
This lecture introduces the fundamentals of gears in mesh, covering gear types, tooth interactions, and how torque and speed are transmitted between gears. Learn the basics of gear ratios and their applications in mechanical systems.
- Power Transformation13:46
This lecture explains the principles of power transformation in mechanical systems, including how power is transmitted, converted, and conserved through gears, shafts, and other components. Key concepts of efficiency and losses are also discussed.
- Statically Indeterminate Structures in Torsion13:31
This lecture explores the analysis of statically indeterminate structures subjected to torsion. Learn methods to determine internal stresses and deformations when torque causes twisting in complex, constrained members.
- Problem 5 - Statically Indeterminate Structures in Torsion10:41
Analyze a statically indeterminate torsion problem for a steel tube bonded to brass core. Compute the steel reaction and plot the shear-stress distribution using tau = t rho / J.
- Combined Loadings - Part 120:51
This lecture covers how structures and materials respond when subjected to multiple types of loads simultaneously, such as axial, bending, and torsional forces. Learn to analyze stress and deformation under combined loading conditions.
- Combined Loadings - Part 233:36
Specify a coordinate system, draw cross section, and move each force to compute moments about x, y, and z, then represent them as torsion or bending and locate compression zones.
- Combined Loadings - Part 324:00
Discover how to compute normal and shear stresses at points on a circular cross-section under combined loading, using centroid, moment and polar moment of inertia, area, and torsion.
- Combined Loadings - Part 49:06
Apply a step-by-step method to compute normal and shear stresses under combined loading, noting zero shear from force at point B and bending and torsion contributions.
- Problem 1 - Combined Loadings25:13
- Continued26:40
- Problem 2 - Combined Loadings28:29
Examine how to determine the state of stress at point A under combined loadings in a circular cross section, computing normal and shear stresses from bending, torsion, and horizontal shear.
- Problem 3 - Combined Loadings21:03
Determine the stress state at point b on a hollow circular cross section by decomposing an inclined 60-degree force and resolving bending and torsion moments about x, y, z.
- Continued14:37
Calculate normal and shear stresses at point B under double bending and torsion, showing compression and about 422 psi net shear via projected forces, area prime, and centroid calculations.
- Problem 4 - Combined Loadings17:50
Determine the smallest distance d to prevent compression at section A when P is applied; use a 200 by 10 mm rectangular cross section and balance bending about the x-axis.
- Stress Transformation - Part 128:09
This lecture covers the theory and calculations behind stress transformations, including how to determine normal and shear stresses on rotated planes.
- Stress Transformation - Part 221:56
- Stress Transformation - Part 310:17
Learn to transform normal and shear stresses under rotation by theta, compute sigma_x', sigma_y', and tau_x'y' from an initial state (sigma_x, sigma_y, tau_xy) using the equation method and Mohr circle.
- Principal Stresses and Principal Planes8:50
This lecture explains principal stresses and principal planes, showing how to find the orientations where normal stresses reach their maximum and minimum values, and shear stress is zero.
- Problem 1 - Principal Stresses and Principal Planes7:34
- Maximum In-plane Shear Stresses7:42
This lecture focuses on calculating maximum in-plane shear stresses in materials under complex loading. Learn how to determine critical shear stress values and their orientations using stress transformation techniques.
- Problem 2 - Maximum Shear Stresses8:34
Identify sigma_x, sigma_y, and tau_xy with the correct sign convention to compute tau_max and theta_s. Use Mohr's circle for finding principal stresses, planes, and the final state.
- Introduction to Mohr's Circle5:58
This lecture introduces Mohr’s Circle, a powerful graphical tool for analyzing plane stress. Learn how to construct Mohr’s Circle to find principal stresses, maximum shear stresses, and stress transformations on rotated planes.
- Mohr's Circle for Principal Stresses and Principal Planes19:42
This lecture demonstrates how to use Mohr’s Circle to determine principal stresses and the orientations of principal planes. Step-by-step construction and interpretation help visualize stress states and identify critical stresses in materials.
- Mohr's Circle for Maximum In-plane Shear Stresses12:48
This lecture explains how to use Mohr’s Circle to find the maximum in-plane shear stresses in a stressed element. Learn to graphically determine shear stress magnitudes and their corresponding planes for design and analysis.
- Mohr's Circle for Rotating Element with Angle Theta15:01
This lecture explains how to use Mohr’s Circle to find the shear and normal stresses for any rotation from the initial orientation.
- Problem 3 - Mohr's Circle with Combined Loadings22:13
Analyze stress transformations using Mohr's circle for a hollow circular cross-section with combined loadings to determine principal stresses, principal planes, and maximum shear stress.
Requirements
- Commitment for Learning Mechanics of Materials: No advanced knowledge or tools are required—just an interest in understanding how materials and structures behave under various loading conditions.
- Access to a Calculator: Students should have a scientific or graphing calculator to solve numerical problems effectively.
Description
Course Description:
Unlock the secrets of Mechanics of Materials with this comprehensive course designed for engineering students and professionals. Whether you're preparing for exams like the FE or PE, enhancing your engineering knowledge, or building a strong foundation in structural analysis, this course has everything you need.
Starting with a review of statics and advancing to complex topics like stress transformation, torsion, and combined loadings, the course systematically covers all the essentials. You'll gain hands-on experience solving real-world problems and designing safe, efficient structures.
What You’ll Learn:
Analyze and solve problems involving stress, strain, and deformation under various loading conditions.
Master techniques like Mohr’s Circle, compatibility equations, and allowable stress design.
Calculate structural properties, including centroids, moments of inertia, and neutral axes.
Evaluate material behavior, including ductility, toughness, and failure modes.
Solve practical engineering problems step by step, preparing you for exams and real-world applications.
What’s Included:
Over 160 detailed lectures covering concepts, examples, and exercises.
Quizzes to test your knowledge and reinforce key concepts.
Step-by-step solutions to problem sets, from basic to advanced scenarios.
Focused sections on bending, torsion, transverse shear, and axial loads.
This course is perfect for:
Undergraduate engineering students in civil, mechanical, aerospace, or structural disciplines.
Professionals preparing for the FE or PE exams.
Anyone looking to refresh or deepen their understanding of mechanics of materials.
With practical problem-solving techniques and clear explanations, this course is designed to help you succeed in your engineering studies and beyond. Enroll today and take the next step toward mastering Mechanics of Materials!
Who this course is for:
- Undergraduate Engineering Students: Ideal for civil, mechanical, aerospace, and structural engineering students who want a thorough understanding of mechanics of materials concepts and their applications.
- Engineering Professionals: Perfect for practicing engineers looking to refresh their knowledge of stress, strain, deformation, and design principles to enhance their skills or prepare for professional certifications like the FE and PE exams.
- FE and PE Exam Candidates: A valuable resource for individuals preparing for the Fundamentals of Engineering (FE) or Professional Engineer (PE) exams, providing in-depth problem-solving techniques and conceptual clarity.
- STEM Educators: Useful for instructors or educators seeking a comprehensive resource to enhance their teaching materials and methods in mechanics of materials.
- Curious Learners and Beginners: Open to anyone with an interest in structural analysis, mechanical properties of materials, and their practical applications, even with minimal prior knowledge. The course starts with a statics review to bridge the gap for beginners.
- Graduate School Applicants: Helpful for students planning to pursue advanced studies in engineering fields, ensuring they have a strong grasp of foundational concepts.