# What is Solid mechanics: Definition and 54 Discussions

Solid mechanics, also known as mechanics of solids, is the branch of continuum mechanics that studies the behavior of solid materials, especially their motion and deformation under the action of forces, temperature changes, phase changes, and other external or internal agents.
Solid mechanics is fundamental for civil, aerospace, nuclear, biomedical and mechanical engineering, for geology, and for many branches of physics such as materials science. It has specific applications in many other areas, such as understanding the anatomy of living beings, and the design of dental prostheses and surgical implants. One of the most common practical applications of solid mechanics is the Euler–Bernoulli beam equation. Solid mechanics extensively uses tensors to describe stresses, strains, and the relationship between them.
Solid mechanics is a vast subject because of the wide range of solid materials available, such as steel, wood, concrete, biological materials, textiles, geological materials, and plastics.

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2. ### I Why does the end of the fracture have a branch? (Fracking)

Hello, I have seen some pictures about hydraulic fracturing, which is injecting water into the ground under high pressure, and when people draw the schematic, it looks like this I am wondering why the fracture will be branched. Thanks!
3. ### I Elastic Constants for Natural Rubber

Hi, Looking for the Elastic Constants for any rubber-like material such as Natural Rubber. It can be inorganic or organic. The constants I am looking for take the form of a fourth-rank tensor. I only need the first order elasticities, not the zeroth or higher (not Cij or Cijklmn.. just Cijkl)...
4. ### What is a recommended textbook for solid mechanics?

Summary: In need of a textbook on solid mechanics Hello, I was asked to teach a class in FE analysis (this is not the issue) for solid mechanics (and, specifically, plane stress and strain) The issue is that some students will be deficient in solid mechanics (long story, I will have the time...
5. ### I What is the function of the air cavity inside drums?

I'm trying to understand the function of the air cavity inside drums. I've read that 'The air cavity inside the drum will have a set of resonance frequencies determined by its shape and size. This will emphasize some frequencies at the expense of others.' Then what are the resonance...
6. ### Engineering Maximum normal stress and shear stress

First, I am trying to find the external reactions in A and B, but I have only one equation relating ##V_A## and ##V_B##, what other relation could I use ? Once I find the reactions, I can find the external moment as well. Then, I may draw the diagram of moments in each cross section and then...
7. ### Glass bottle with a prolonged neck that continues into the inner space

Is it possible to create following two shapes from glass using currently known glass mass production techniques? Shape #1: bottle with a prolonged neck that continues into the inner space, like this (cross section): | | | | /| |\ / | | \ / \ / \ | | |...
8. ### I Stresses Caused By Deformation For Bending

Hi. Say you apply a moment on a beam and bend it into an arch. If you take a free body diagram of a section of the beam you would need normal stresses in the radial direction to balance the forces: I have never seen this brought up before though -- is it correct logic? Also, is this sort of...
9. ### I Find Frequency of Block Oscillation Due to Shear Force

Hi. I'm trying to determine the frequency of an block (roughly a rectangular prism) when the oscillation is due to a shear restoring force. Here is a diagram: In the derivation, ##\rho## is the density of the block,##G## is the shear modulus of the block, ##y## is the elevation of the element...
10. ### Deformation under eccentric shear stress

Hi, Starting with an example to clarify what I am looking for. Assume an extension force applied on a distance from the centroid/neutral axis of a body: see attached, please. As result, bending force besides the tensile force will be generated in that body as presented in section A-A in the...
11. ### Stress Used in Lagrangian Equation for Solid Mechanics

Bathe (reference below) outlines the updated Lagrangian (UL) and total Lagrangian (TL) approaches using the second Piola Kirchhoff (PK2) stress. Others (i.e., Ji, et al. and Abaqus) define the UL and TL formulations in terms of the Kirchhoff or the Cauchy stress in rate form. This form requires...
12. ### Force-Deformation Equations Application

Just found this forum--hope there isn't a max post limit haha. I have been a bit stumped on this, but when doing problems about deflection and axial loadings, I am confused when to use which equation. I think I know that axial member need to be 2 force members, loaded only at the ends, and...
13. ### Split Hopkinson pressure bar data

Currently coding a wave separation script for the split hopkinson pressure bar. Is there a place I can get raw data for the split hopkinson pressure bar to test my code?
14. ### Large deformation in solid mechanics

Hi initially I am aware that large deformation in solid mechanics requires non linear strain theory in the lieu of infinitesmall strain theory. But I wonder that if we can approximate large deformation of material using infinitesmall strain of small elements employing and summing linear strains...
15. ### Thermal expansion of each dimension of a solid

Hi, I am trying to work out how much each dimension of a solid (for instance an annular disc) made out of steel changes assuming that the solid is heated uniformly and is not constrained at any of its boundaries. Am I right in saying that, the linear expansion equation L = L_0 (1+ α ΔT) can be...
16. ### Should I learn fluid mechanics or thermodynamics

I am graduate student from structural mechanics of solids and need to learn 1 course from fluids and thermal group which includes fluid mechanics or thermodynamics+heat transfer. I am unsure which one would be better to learn, especially which would be helpful in future for solid mechanics. Can...
17. ### Physical interpretation of the "total potential energy"

The principle of minimum total potential energy is frequently used in solid mechanics as an elegant way of deriving the equilibrium equations for an elastic body under conservative forces. This method states that out of all the possible displacement fields that fulfill the boundary conditions...
18. ### Calculus: Verify Thick Walled Cylinder Equations

Homework Statement I have a system of two ordinary differential equations as shown below. I have to prove that the Lame's exact solutions for a thick walled cylinder loaded by internal pressure satisfies the equations. The next step is to integrate the equations to obtain an equation for U...
19. ### I Substituting a solid body with mass points

I ran into the following problem, and stuck for a couple of days now. I have a solid body, rigid and and has uniform density. Its mass M, the location of the center of gravity x_M, y_M, z_M and its inertia matrix is known: Jx Jxy Jxz Jyx Jyy Jyz Jzx Jzy Jz I have to write an algorithm...
20. ### Stress in a rod with a hole for pin-joint

If a rod is in compression, will the minimum area on rod ( the section where there is a hole for pin) stress free? What if the rod is in tension? The rod BC is in compression and the boom AB is in tension? http://imgur.com/a/6asfB
21. ### Equivalent Bending Moment due to Impact Formula?

Hi guys and girls, I've been working on this problem for a little while now but I'm not really getting the result that I want. This is what I have: I have what is essentially a big pair of vice grips controlled by a hydraulic cylinder. The cylinder opens and closes both arms of the vice grips...
22. ### Airy's stress function for a cantilever beam

I have to calculate Airy's stress function for a cantilever beam made of two different material along its length. The young's modulus of the first half is E1 and E2 for second half. The beam is made such that these materials are joined to each other one after other along its length. At the...
23. ### Solid Mechanics Q: Textbook source for image?

Hi everyone, Does someone know from which textbook the question below was taken from? The only given data the i found is q1=π*sin(πx/2). Thanks:)
24. ### Fatigue Analysis: Maximum & Minimum Stress

Whether we are using Soderberg or Goodman line; it is two dimensional Cartesian coordinate system in which x-axis is the mean stress and y-axis is stress amplitude. For them to calculate we have two values one is maximum stress and other is minimum; I found on Quora.com that they are not...
25. ### Stress strain diagram of mild steel -- gauge length made half

All we know the usual stress strain diagram obtained from tensile test from universal testing machine. As modulus of elasticity is material property that means till proportional limit slope will not change. As it is not a force vs elongation curve that means there will be no re-scaling to be...
26. ### Reliability of Upper/lower yield point in tensile test.

Some metal give two yield point in stress strain diagram. One is called Upper yield point and Lower yield point. Why lower yield point is considered as more reliable. I can think of Upper yield point is much more dependent upon experimental apparatus settings. So why lower yield point is much...
27. ### Conformability elastic material compressed on a wavy surface

Hey there, I'm struggling in finding the useful equations to determine some conformability parameters for a finite elastic material (EPDM) compressed on a rigid slightly wavy surface. I would like to optimize the thickness of the elastic material in terms of indentation depth and thus contact...
28. ### Calculating deflection with rotation about center support

I am preparing for a qualifying exam for my PhD program and am looking at some of the old tests from previous years (as supplied by the school for study/prep material). I have come across a deflection problem that has me stumped, and I might just be overthinking it. The problem:
29. ### Solid Mechanics - Stress-Strain diagram - absorbed energy

Homework Statement 1.The maximum energy (per unit volume) that can be absorbed by the steel alloy without sustaining permanent deformation is _______ lb/in^2 1.4. The maximum energy (per unit volume) that can be absorbed bythe steel prior to fracturing is _______ kip/in^2. . Homework...
30. ### Finding the shear stress and angle of twist in hollow shaft

MODERATOR NOTE: THIS THREAD WAS ORIGINALLY IN ANOTHER FORUM, SO THERE IS NO TEMPLATE. I have a hollow shaft made of a titanium alloy, Shear Modulus "G". The shaft has a wall thickness of 3.2mm and an inner diameter of 20mm. The shaft looks as show in the attached image. A torque T of 232 Nmm...
31. ### Calculating shear stress in a beam?

The equation for shear stress as I know it is VQ/It where V is the shear force, Q is the first moment of area(?), I is moment of inertia and t is the length of the section in question. My question is, is there a general formula for Q? In my Solid Mechanics notes I've written that Q = ∫y.dA but...
32. ### Solid Mechanics - Uniqueness of Plane Stress State

Homework Statement My textbook says that the state of plane stress at a point is uniquely represented by two normal stress components and one shear stress component acting on an element that has a specific orientation at the point. Also, the complementary property of shear says that all four...
33. ### 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...
34. ### Solid Mechanics Stress Blocks- Principle blocks

Hey guys, I would just like some confirmation that I got this question correct. Homework Statement For the stress block shown in Figure 3a, using the stress equations; a) Calculate the stresses sigmax' sigmay' and taux'y' on a stress block rotated 15° clockwise from the x-y axes...
35. ### Simply Supported Beam Stress Block Selection

Homework Statement Hey guys, I have a test coming up soon, and our lecturer gave us a sample test. I am working through it, but we have not been given any answers to confirm if what we are doing is correct. The Question: "For the simply supported beam (with upstand) shown in...
36. ### Need verification on a couple of solid mechanics exercises

Like the tittle says.. I am practicing and wanted to make sufre I did it correctly. Forma this excersice the only doubt es en the las parte ( parte 5)... I am not sufre but i think I need to use .005 rather than .05
37. ### Why Do We Multiply Distance, Mass, and Gravity in Sum of Forces Calculations?

Ok, so the formula I know to find weight is W=mg. Why is it that when doing a sum of forces in z they multiply (distance)(mass)(gravity) and not simply sum the gravity force that is mg?
38. ### Solid Mechanics- Ultimate Load in truss.

Homework Statement A 3/4-in.-diameter rod made of the same material as rods AC and AD in the truss shown was tested to failure and an ultimate load of 29 kips was recorded. Using a factor of safety of 3.0, determine the required diameter (a) of rod AC, (b) of rod AD. Homework Equations...
39. ### Solid mechanics thermal stress of infinite cylinder

Homework Statement My problem is to calculate the Thermal stress of a Cylindric shell with inner radius a and outer radius b the inner surface is experiencing Temperature T1 and the outer surface is experiencing T2 with T1>T2 assuming that the linear thermal expansion coefficient is a, the...
40. ### Solid Mechanics Stiffness Question

Homework Statement A 0.5m high and 100mm diameter post is to be made from concrete reinforced by 10mm diameter steel rods. How many steel rods should be used if the axial stiffness of the post is to be at least 2000kN/mm? Homework Equations n = number of steel rods D = diamater of the post d...
41. ### Solid mechanics challenge question

Hi all! Good evening Here is the Question: This question is given as a challenge extra credit task, and is a part of a course called solid mechanics 2 that deals more with shear strain and strain matrices. While trying to translate the question I used the term "strength" instead of...
42. ### Solid Mechanics - Force in a bolted assembly

A bolted assembly consists of a steel bolt A, a brass tube B and a nut C. The nut is turned so that it just secures the tube, and then is tightened one extra turn. Determine the resulting force Fs (in kN) in the steel bolt. The initial length of the tube is L = 158 mm, and the screw pitch is 1mm...
43. ### Solid Mechanics, calculating reaction forces and M(X) for a cantilever thing

Homework Statement Homework Equations M = F * D The Attempt at a Solution For a, I need to find the reaction force on the right side. So what I first did was make the sum of the moment on the left equals zero. 0 = M_0 + r_y * L. r_y = \frac{-M_0}{L} I think this is right...
44. ### How to Determine the Ratio of Inner to Outer Diameter in a Stressed Pipe?

Basically, my problem is small part of a bigger assignment, but I'm completely stuck at this point. This is really a math problem, but I figured I'd post it here anyway considering I might have misunderstood the physics. Homework Statement A vertical pipe is subjected to a axial force of...
45. ### Solid Mechanics: Cantilever Beams & Loads on Neutral Axis

Hi, In a cantilever beam with a load on the free end, at a point on the neutral axis, will the normal stresses (due to bending stress and axial stress) be zero? Or am i wrong? And if i was to draw a Mohr circle for that point at the neutral axis, would the center of the circle be the origin? I...
46. ### Solid mechanics (shear stress) question

Hi, if the shear stress on an element in a solid is SAy/bI, where S is the shear force and y is the distance from the neutral axis, what value of y do i use if the point I'm calculating is on the neutral axis?
47. ### Solid mechanics, castiglianos second theorem

http://img237.imageshack.us/i/lahaka.jpg/ http://img237.imageshack.us/i/lahaka.jpg/ So... I need to determine the deflection of the beam under applied force P due to flexural deformation using castiglianos second theorem. Simply, delta = dU / dP How do I determine the strain energy U for the...
48. ### Solid Mechanics: Calculating Stress for Aluminium & Steel

now i am looking for the stress \sigma for the aluminium and for the steel i would want to say simply \sigma=F/A but i need to somehow take into account the types of materials and their elasticity, i think that hookes law could help me here but i don't know the strains also how do i take the...
49. ### Solid Mechanics questions - A new challenge

Solid Mechanics questions - A new challenge :) Hi all :wink: I got 3 new questions that need to be solved in about 3-4 days as part of a 'challenge' homework. Those who solve correctly will basically get their names read out loud on the next lecture but I do it to understand the material of...
50. ### Solid Mechanics Question - Help

hi all :biggrin: i apologize in advance for the poor englsih, the question is translated from another language. A round beam (radius R) is harnessed on the left side to a wall. The beam is made up of two parts glued together by a thin layer of glue - the attachment plane is described in...