What is Mechanics of materials: Definition and 103 Discussions

The field of strength of materials, also called mechanics of materials, typically refers to various methods of calculating the stresses and strains in structural members, such as beams, columns, and shafts. The methods employed to predict the response of a structure under loading and its susceptibility to various failure modes takes into account the properties of the materials such as its yield strength, ultimate strength, Young's modulus, and Poisson's ratio. In addition, the mechanical element's macroscopic properties (geometric properties) such as its length, width, thickness, boundary constraints and abrupt changes in geometry such as holes are considered.
The theory began with the consideration of the behavior of one and two dimensional members of structures, whose states of stress can be approximated as two dimensional, and was then generalized to three dimensions to develop a more complete theory of the elastic and plastic behavior of materials. An important founding pioneer in mechanics of materials was Stephen Timoshenko.

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  1. Q

    Statically indeterminate problem

    Homework Statement Calculate the stress in every segment of the system. AD and BC are laton and AB is steel. Homework Equations geometry compatibility-δ(A/D) +δ(A/B) - δ(C/B) = 0 F(D) - F(C) - 50 =0 The Attempt at a Solution I supossed that DA and BC are in compression and AB is in...
  2. T

    Factor of Safety - Mechanics of Materials

    Homework Statement Rigid beam ABC is supported as shown in the figure. The pin connections at B, C, and D are each double shear connections, and the ultimate shear strength of the pin material is 640 MPa. Tie rod (1) has a yield strength of 350 MPa. A uniformly distributed load of w = 11 kN/m...
  3. xortdsc

    Simulation of internal mechanics of materials of high restitution

    Hello, just for some basic understanding I wrote a (1D) numerical simulation to investigate the internal mechanics of collision impact in different materials. For a start I work with a really simple model which consists of: - basic elements (circles of fixed radius and mass and their current...
  4. jtmbii

    Axial Deformation and Poisson's Ratio Calculation

    I've been studying this problem, trying to understand the given answer, but still no success. Homework Statement <<provided in attachment>> Homework Equations Longitudinal Strain Latitudinal Strain: where is the amount the radius contracts, r is original radius Average Normal Stress...
  5. S

    How Does Internal Pressure Affect Yielding in Steel Tubes?

    Homework Statement A long circular steel tube having a mean diameter of 254 mm and 3.2 mm wall thickness is subjected to an internal pressure of 4.83 MPa. The ends of the tube are closed. The yield stress of the steel is 227 MPa. Find the additional axial tensile load F which is needed to...
  6. Chacabucogod

    Mechanics of materials beam Problem

    A 1-ton wall hoist consists of a horizontal beam, supported by a tension rod at 30 deg, as shown. The rod is to be designed with a factor of safety 5 with repeat to its yield point of 30,000 PSI. Determine its necessary cross section S=F/A 30000/5=6000PSI -2000+Rsin(30)=0...
  7. C

    Mechanics of Materials - Deflection of an L shaped beam

    Homework Statement A. determine the deflection at point A in the X and Y direction. B. determine the maximum normal stress in the beam C. determine the maximum shear stress in the beam Homework Equations δ=(PL/EA) (possibly?) δt=αΔτL d2v/dx2 = M/EI dM/dx = V δab=δx*cosθ +...
  8. D

    Mechanics of materials question, angle of twist in shaft

    Hello, I'm studying machanics of materials.. I'm at the chapter that handles the angle of twist in shafts. There's one exercise that I get the most part of, but there's just a tiny part of it that I don't get! here's the exercise...
  9. B

    Mechanics Of Materials Stress Problem

    Homework Statement Here is a link to a picture of the problem: http://imgur.com/5nOnpJE Click on the picture to make it bigger, and readable!I need to find the angle that the two rods will have the same stress. We are talking about normal stress here! Homework Equations \sigma = Force /...
  10. R

    Tensor based mechanics of materials books

    I was seaching mechanics of materials books, but i need them to be tensor based. Any sugestions?
  11. E

    Mechanics of materials centroidal question

    Homework Statement a beam is 12 cm wide and 10 cm long. Find the neutral axis, the area centroid and the distance between them. Homework Equations Yc=h/2 The Attempt at a Solution Yc=10/2=5 cm. I can't seem to find the area centroid of a rectangle. Any help? Thanks!
  12. G

    Mechanics of Materials; I regarding this very fundamental problem.

    Why would the force P not always be equal to 60 kips? (I mean, since the structure is in equilibrium, and the members are rigid, can't we shift the two forces of 30kips each to the line of action of force P and conclude that P is always 60kips?) Thanks for your time.
  13. G

    How Do Forces Differ in Multiple Members of a Structure?

    Homework Statement (please see the attachment) Homework Equations σ=F/A The Attempt at a Solution I just can't figure out how to find the forces in the two members. Actually I thought the force in both members will be the same, but according to the problem statement it clearly...
  14. P

    Statics - Mechanics of Materials, check my work please?

    Could someone please check this for me? I attached a rough free body diagram of the whole frame. Any help is appreciated. Homework Statement The member ACF of the frame loaded as shown is connected to member BCD by means of a smooth peg and slot C with force P = 930 N at point D...
  15. Femme_physics

    Mechanics of Materials - Angle of Torsion

    Homework Statement http://img820.imageshack.us/img820/3373/torsionquestion.jpg Homework Equations (In the solution) The Attempt at a Solution I got M(max) and d correct. I can't get the angle. But I'm using the formula exactly as is. What's wrong...
  16. Femme_physics

    Mechanics of Materials - Torsion

    Homework Statement http://img840.imageshack.us/img840/736/mmaterials.jpg Homework Equations http://img18.imageshack.us/img18/8739/releq.jpg The Attempt at a Solution http://img845.imageshack.us/img845/7017/pitul.jpg The answers turn up (a) 56.6 MPa and (b) 36.6 MPa so I'm...
  17. Femme_physics

    Mechanics of Materials - Shear and Compression

    Homework Statement http://img62.imageshack.us/img62/9815/mechmatt.jpg P = 235 kN d = 50mm (diameter of the axis) t = 20 mm t1 = 12 mm Safety coeffecient = 2.0 σy = 320 MPa Check the axis for strength (shear and compression) Homework Equations...
  18. N

    Mechanics of Materials - is this correct?

    Homework Statement Homework Equations The Attempt at a Solution I was attempting to solve this exercise, but since I have no answers, I have no way of knowing if it's correct. Any help Is more than appreciated
  19. Femme_physics

    Mechanics of Materials - Where's my mistake?

    Homework Statement http://img85.imageshack.us/img85/6346/missrd.jpg Across the axis of a steel rod act 3 forces: F1 = 80 kN F2 = 50 kN F3 = 30 kN Crossection area of rod = 4cm2 What are the forces that are being made a the different parts of the rod, and what will be it's overall...
  20. R

    How Do You Calculate Maximum Torque in a Hollow Shaft?

    Homework Statement A hollow shaft has torque being applied on both sides. The angle of twist is 50 degrees, the diameter is 100 mm, the thickness t has 5 mm. We are given that the allowable stress is 120 MPa, and the allowable shear stress is 50 MPa. We are asked to solve for the...
  21. Femme_physics

    Mechanics of Materials basic exercise

    Homework Statement A graded steel cylinder AISI 1030 is connected to a wall and loaded with axial forces. http://img542.imageshack.us/img542/3959/fbd1.jpg Given: F = 30 [kN] d1 = 35mm d2 = 20mm Elastic Model: E = 2x105 MPa Safely coeffecient: 2 Yield strength limit: 440...
  22. B

    Trussel buckling,question from mechanics of materials

    Ok,first of all ,I'm sorry for any further language barrier things,I study in a non-English speaking university,and I might do a mistake in translating some technical terminology. So,the problem is from mechanics of materials,buckling loads.This subject gives me nightmares as it is,I can barely...
  23. J

    Hibbeler Mechanics of Materials

    Hey guys I'm looking through my Mechanics of Materials book (Hibbeler 8th ed.) and am quite confused at the section on shear and moment diagrams. I thought I grasped it very well in statics but I guess I was wrong. Anyways I am looking at Example 6.4 and it asks for the shear and moment...
  24. G

    Mechanics of Materials - Deflection of a rigid bar

    Homework Statement http://img.waffleimages.com/5b5524d885644e9f1c76a800c4b0701a0606268a/problem6.jpg (The image will not work unless it is copied and pasted into the address bar) I am given this drawing and stress v strain diagram, and am told to find the deflection, ∂, at 4 (the end of...
  25. J

    Mechanics of Materials Explanation

    I was reading through my mechanics of materials book (Mechanics of Materials 8th ed. R.C. Hibbler) learning about stress and came across example 1.6 pg. 28. while most of the example makes sense the last bit of part b) confused me. I am unsure as to why for Pcd he only showed the 22 kN force...
  26. C

    Online Mechanics of Materials Resources for Basic Equations

    Does anyone have any good online reference sources that derive the basic equations from Mechanics of Materials such as angular deflection of beams under torsion, stress on cross section due to moments, etc. all the easy basic stuff. I took those classes a long time ago and I don't remember...
  27. W

    Mechanics of Materials: Torsional deformation at free end with torque at middle

    Homework Statement A circular shaft AB has a torque T acting at the middle of the shaft, defined as plane C. Shaft end A is fixed while shaft end B is free to rotate (mounted in a thrust bearing). Finding the twist angle from A to C is not difficult, but the question requires that the twist...
  28. S

    Mechanics of Materials: Torsion

    Homework Statement A shaft fixed on both ends is shown below. It is made of a steel tube, which is bonded to a brass core. A torque T_D is applied at location shown. The tube is fixed at both ends. [PLAIN]http://img202.imageshack.us/img202/2940/problem2eb.jpg Show that the fraction of...
  29. S

    Mechanics of Materials: stress due to thermal expansion

    Homework Statement The magnesium allow tube (AM1004-T61) AB is capped with a rigid plate. The gap between E and end C of 6061-T6 alluminum alloy solid circular rod CD is d[m] when the temperature is T_1 degrees celcius. [PLAIN]http://img27.imageshack.us/img27/8867/problemwn.jpg The...
  30. I

    Mechanics of Materials questions

    Hello Everyone I have a mechanics of materials questions which I have been stuck on for hours, I just can't figure it out. Attached is the questions. I know the formula for deflection which is PL/ AE but what do i do with that formula in this situation? Any help would be...
  31. K

    Need a Mechanics of Materials book

    Hi I need a companion text for my intro Mechanics of Materials book by Beers. I am somewhat frustrated in the inconsistency in explanation it will review a statics topic in excruciating detail then gloss over an important detail. I feel with another book in hand I should be able to conquer...
  32. K

    Normal Stress question - Mechanics of Materials

    Homework Statement Conceptual question - When considering beam connected to something say a wall by a cylindar shaped pin, why is it when the beam is in tension near the pin the stress is high as the load is applied over a smaller cross section (normal cross section - profile of the pin) but...
  33. I

    Mechanics of Materials Torsion Test Help

    Homework Statement Hello, I am writing up a lab for a torsion test that we performed on mild steel (ductile material) and cast iron (brittle material). For each of the materials, we must find: • For Mild Steel: - Torque vs. Angle of Twist per unit length. - Shear Modulus - Shear Yield...
  34. M

    Mechanics of materials ques / stresses in beams

    Homework Statement refer to attachment Homework Equations The Attempt at a Solution I am completely confused at where to start can someone get me going in the right direction here as to one of the answers.
  35. M

    Mechanics of Materials - Internal Moment

    Homework Statement Hi everyone. I am attempting to calculate the internal moment at point B about the y-axis. I have correctly found everything else. My calculations: Weight of 500mm section of pipe = 58.9N Weight of 400mm section of pipe = 47.1N Vertical reaction at A = 58.9 + 47.1 = 106N...
  36. djeitnstine

    Mechanics of Materials & Principal of superposition

    Homework Statement A steel tube with a 32mm outer diameter and a 4mm thickness is placed in a vice and is adjusted so that the jaws tough the ends of the tube without exerting any pressure on them. The two forces shown are then applied to the tube. After these forces are applied, the vice is...
  37. 2

    Solve Section 9.2 Probs 1-4 7th Ed Mechanics of Materials

    I have Mechanics of Materials By James M Gere the 5th edition. My class uses the 7th edition which has been virtully the same so far. I have to do section 9.2 problems 1,2,3,4 for homework from the 7th edition. In the 5th problems for chapter 9 start on section 9.3. So i was wondering if anyone...
  38. S

    Simple Mechanics of Materials: Deformation and Torsion

    Homework Statement Shaft AB is fixed at point A and is subjected to a torque T = 2.5 kN·m applied at point B and an axial force P = 30 kN applied at point C. The actual shaft specifications (type of material, prismatic / changing cross sections are left up to us and is NOT the point of...
  39. S

    Mechanics of Materials: Simple moment question?

    Homework Statement A long retaining wall is braced by wood shores set at an angle of 30 degrees and supported by concrete thrust blocks. The shores are evenly spaced, 3m apart. For analysis purposes, the wall and shored are idealized. Note that the base of the wall and both ends of the...
  40. S

    Question (Mechanics of Materials)

    Hi guys, I am attaching a pdf file with the respective question it might be silly for many of you, but I would rather this question now, and move on with the problem. The pdf file is from a class from mechanics of materials, I understand the procedure and how formulas are plugged and how the...
  41. S

    Understanding Mechanics of Materials: Derivation of Strain Energy

    I have a problem understanding what is going wrong with a simple derivation for strain energy. Problem: Assume a prismatic bar of length L where the elastic region is assumed. If it is hanging vertically its own weight produces some strain. If all the work goes into strain energy the...
  42. Astronuc

    Exploring Mechanics and Materials to Deformation Mechanism Maps

    This material forms a bridge between mechanics and materials science. MIT Open Course - http://ocw.mit.edu/OcwWeb/Materials-Science-and-Engineering/3-11Mechanics-of-MaterialsFall1999/Modules/index.htm This is a fairly general course. A more specialized area - DEFORMATION-MECHANISM...
  43. M

    Calculating Minimum Thickness for Aluminum Alloy Tube Supporting Steel Rod

    (Q) An aluminum alloy (E=73GPa) tube A with an outer diameter of 75mm is used to support a 25-m-diameter steel (E=210GPa) rod B, as shown (in the attachement). Determine the minimum thickness t required for the tube if the maximum deflection of the loaded end must be limited to 0.40 mm. I...
  44. D

    Mechanics of Materials II - Mohr's Circle

    Homework Statement For an element [Stress Block], determine the range of values of \tau_{xy} for which the maximum tensile stress is equal to or less than 60 MPa. Given in the provided figure: \sigma_x = -120 MPa \sigma_y = -60 MPa Homework Equations \sigma_{ave} = \frac{\sigma_x...
  45. M

    Need Solutions Manual for Mechanics of Materials

    Need Solutions Manual for "Mechanics of Materials" I am trying to locate someone that has a solutions manual for "Mechanics of Materials" Edition 4 by Beer, Johnston and Dewolf...copyright about 2005. If anyone has one or happens to know where to get one or where to look I would be...
  46. Cyrus

    Mechanics of materials dx,dz,dz

    Im taking mechanics of materials. One of the things they talk about is cutting out a small elemental cube of a rigid body, that has sides dx,dz,dz. Is it always true that dy,dx, and dz have the same infinitesimal size? I thought that they would not necessarily be the same size, which could give...
  47. Cyrus

    Mechanics of Materials: Design Analysis of Structural Elements 4th Ed.

    Hey, I just bought my book for mechanics of materials from the book store. Apparently its used in teaching statics and mechanics of materials all in one. I already took statics with Hibbeler, and I really did enjoy that book. It was VERY thorough. I looked through this books statics and felt...
  48. Cyrus

    Design Analysis of Structural Elements: Mechanics of Materials Review

    Hey, I just bought my book for mechanics of materials from the book store. Apparently its used in teaching statics and mechanics of materials all in one. I already took statics with Hibbeler, and I really did enjoy that book. It was VERY thorough. I looked through this books statics and felt...
  49. D

    Mechanics of Materials Bending Stres Problem

    Mechanics of Materials Bending Stress Problem Hi, I have a homework problem for mechanics of materials involving bending stress. Here is the exact wording: "Show that the maxiumum bending stress for a beam of rectangular cross-section is Omax = Mc/I [(2n + 1) / (3n)] if instead of...
  50. Astronuc

    ME 354 Mechanics of Materials Laboratory

    University of Washington - Mechanical Engineering Department Course Notes Chapter 1 Introduction Chapter 2 Stress, Strain and Constitutive Relations Chapter 3 Beams: Strain, Stress, Deflections Discontinuity functions Comparison of...
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