Questions tagged [solid-mechanics]
Solid mechanics deals with the solid bodies subjected to various type of loading and internal forces generated due to this loading.
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Why are two wires used in railway overhead equipment?
While watching the train videos, I came across these overhead wires. After searching on the internet, I found that both catenary and contact wires carry the same voltage and are connected by vertical ...
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Why does a jumping rope have no bending stiffness and compression stiffness?
Can anyone just tell me that why doesn't a jumping rope, or any other kind of rope, have any bending stiffness? If I hold one end of the rope in my hand, the rest of the rope will just fall. It won't ...
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Calculating the bending moment ($M$) of a beam as it relates to stress ($σ$) and strain ($ε$)?
I am trying to learn how to work out the bending moment for progressively complex systems to model a beam. I am assuming only one axis of motion (transverse = $y$).
For the basic equation of material ...
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Why shouldn't we use Bernoulli beam theory if deformations and rotations are large?
I was going through the basic assumptions made by Bernoulli beam theory. I realized that one of the most important assumption in this theory is that the deformations and rotations of the beams are ...
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Torsion and Bending stress calculated from deflection
I need help to check a calculation I did. I want to know if it is possible to use this method or if I am using an assumption which is wrong. Let me explain the problem, a beam with length $l$ is ...
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How is motor torque related to capstan equation?
I know that capstan equation relates $T_{in}$ and $T_{out}$ as $T_{out} = T_{in}e^{u \cdot F_c}$, where $u$ is friction coefficient and $F_c$ is wrap (slip) angle. In my situation, the capstan is ...
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What is stress stiffening in Finite Element Analysis?
In a Finite Element Analysis, if we turn ON the geometric non-linearity, it also takes into account the stress stiffening if any structure is undergoing it. That is what I have read in the literature.
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Why is the thin-walled cylinder more likely to experience failure along its axis than along its hoop/circumference?
I was watching a YouTube video to understand the concepts of hoop/circumferential stress and axial/longitudinal stress in thin-walled cylinders and their formula derivation.
So the formula of the ...
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What exactly is Hooke's law defined for?
I used to think that Hooke's law was a relationship between how much a bar under uniaxial loading deformed and the internal force (per unit area) that developed within that bar. But this clearly isn't ...
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Bending behavior of built-up C-Channel
I am analyzing a built-up C-channel for bending purposes (2 point loads of 1200 N each @ 30 cm symmetrically from the CL). The flanges are made of a different material than the web, they are also of a ...
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Is there any formula to model the effective Young's Modulus of a fluid-filled spherical shell?
I am creating composites of a host epoxy and filler particles which are thin-walled fluid-filled shells. Using the Halpin-Tsai equations, for example, I can predict the bulk composite Young's modulus ...
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I don't understand a simulation result of frequency vibration analysis of ultrasonic tranducer
I am building a ultrasonic transducer like this (with double-exponential (75%-25%) match and 2 ring PZT8 50x20x6.5 (for the moment I do not take account of pre-stress on bolt) :
When I simulate the 2 ...
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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 (...
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Column Buckling Boundary Conditions -- Welded Tubing Practical Application?
I'm trying to do some calculations for a personal project. I'm trying to understand column strength / buckling. My questions relate to Effective Length Constant, which is based on Boundary ...
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Why do we always need to calculate the 'Moment of Inertia' about neutral axis for bending?
I was having a look at the bending stress derivation in few of the books. The derivation indicates how each of the element in the bending stress equation is derived into that equation. However, for ...
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Why does concentrated shear force on a beam influence the whole beam?
This might be a silly question but can someone explain how this shear force on the right side of the beam causes Qy throught the whole beam?
I understand it mathematically but not conceptually so I ...
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Moments of Fixed-Fixed Beam
I have a quick question related to the topic of mechanics of materials.
If I were to have a beam that is fixed at both ends and has a central point force, do moments develop at the fixed supports?
e....
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What is the significance of brittle materials and why do we use them?
What is the significance of brittle materials and why do we use them?
As you can see in the stress-strain curve, brittle materials have extremely low plasticity, in which cracks can initiate without ...
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Do all structures deform if put a load on them?
Suppose I have a concrete wall in front of me and I push on it, now it seems that I do work and the energy has magically disappeared.
I am trying to figure out how this works, the explanation I ...
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Difference between Stiffness (K) and Modulus of Elasticity (E)?
Stiffness (F=Kx) is the extent to which an object resists deformation in response to an applied force. Elastic Modulus (E=Stress/Strain) is a quantity that measures an object or substance's resistance ...
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Interpretation of dimensionless numbers as ratios of forces
How can the dimensionless numbers like reynolds number etc be interpreted as ratio of the various forces? The explanation given by most sources in this regard seems quite unsatisfactory and not much ...
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Is bending moment along a beam independent of the cross sectional area of the beam?
We know this that if the a cantilever beam (of any cross section) is fixed at one end and a transverse force is applied on the other, then it will bend. However, we just casually assume that the ...
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What is the significance of hinge in the internal structure of the beam?
I had come across a question on shear force and bending moment diagram where a cantilever beam with a roller support at point C is given and the portion beyond point C in overhang. Does this hinge act ...
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Which yield strength should I use in FEA in ANSYS; Engineering or True?
Attached is a figure to illustrate the difference in the value of yield strength as observed from the true stress/strain curve and engineering stress/strain curve. While conducting FEA in ANSYS for a ...
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Boundary condition at supported end of a rod
I have one end of a rod held in a hole of a 'rigid' part with no clearance, while the other end is loaded with a force. I have shown 3 simple reaction-force models in the picture.
If my intent is to ...
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What's the difference between linear and nonlinear continuum mechanics?
I have been recommended to read a book about nonlinear continuum mechanics, but when I have taken a look at the table of contents, I found myself familiar with most of the concepts in the book since I ...
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What should be the relation between flange length and web thickness for an optimum I - beam?
While learning about I-beams I became curious to know if there is any relation between the flange length and web thickness of I-beams or if its arbitrary.
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Understanding Castigliano's First Theorem Proof
I'm trying to understand the derivation of Castigliano's first theorem in the book Fundamentals of Finite Element Analysis by David V. Hutton, which goes as follows.
The strain energy is defined as
$$...
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Why does local derivative and convective derivative only apply to spatial descriptions?
In continuum mechanics, why does local derivative and convective derivative only apply to spatial descriptions?
Is it because in the material description, the motion focuses on the particles, and not ...
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Shear flow for unequal leg channel
How does the sine part i.e. $\dfrac{\ell\sin(\theta)}{2}$ appear in the calculation of shear flow ($q$)? I mean, if I'm not mistaken, the sine part is the distance from the x-axis to point D, but how ...
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Compressional Strain Definition
Strain in the x and y directions are defined by the following equations:
$ε_x=\frac{du}{dx}+\frac{1}{2}[(\frac{du}{dx})^2 + (\frac{du}{dy})^2]$
$ε_y=\frac{dv}{dx}+\frac{1}{2}[(\frac{dv}{dx})^2 + (\...
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Why does the torsion in a circular bar result in shear stress along the axial direction?
In the case of pure torsion, how does a differential area on cross-section of the cylinder with dx length undergo a shear force that is perpendicular to the cross-section ?
I can understand that a ...
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Should we use Hooke's Law (that linearly relates stresses to strains) if the stiffness of body is changing during deformation?
Assume I have a slender cantilever beam, fixed at one end and force applied on the other. Now, during the deformation, we know that the beam's stiffness is going to change and the force-displacement ...
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What happens to load bearing capacity during the plastic region for a ductile material?
Attached is a picture of a typical isotropic ductile material. Can anyone please tell me what happens to the load bearing capacity in the structure in each of the sub-regions under plastic deformation,...
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What's the difference between Strain tensor and deformation gradient tensor?
Why do we need to define the strain tensor if we already have a tensor that describes the deformation between relative particles in the continuum which is the deformation gradient tensor?
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How do hooks/bends cause bearing stresses in reinforced concrete?
Can someone please explain the exact mechanics of development of bearing stresses in concrete on account of bending of steel reinforcement and/or providing of hooks at the beam-column junction for ...
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Latch Mechanics
I want to make a sprung latch mechanism which keeps a door in place until a certain force is applied to the door. In the diagram attached, the force the door must release at is Fd, and the latch ...
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Shape of a beam that is bowed under compression?
Suppose you have a uniform beam, such as a piece of plywood that is 4 feet long, six inches wide, and half an inch thick. Suppose you cause it to bend by attaching, for example, a string under ...
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Thermal Expansion and Stress in a Heated Beam
Consider the case of a beam that is supported in such a way that expansion can occur freely. Suppose that the beam is heated in such a way that the temperature varies with the depth of the beam. Let $...
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Magnetic Force - Point of Load
I am using a Magnet like this in an assembly and I am trying to calculate the torque in point P2 (see picture below) resulting from the attraction force F between my magnet and the steel part.
As I ...
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Finding the Shear Center for a Beam with 1 Axis of Symmetry
I am trying to solve this problem of finding the shear center for the given beam and I have found that e = 35.94 mm, however the solution that was shared with me, had the answer of 39.17 mm.
My method ...
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Why the variable "r" appears in circumferential force balance for a membrane
I am trying to understand a force balance for an inflating membrane (reference cited at the bottom of the post) and can't figure out why there is an "r" in the circumferential balance.
The ...
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Deformation gradient tensor from particle displacements in an inflating material
I don't have a mechanics background, but am trying very hard to read and understand how to approach this problem. I am struggling with understanding what's "correct" or the basic process of going from ...
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Determinating Reactions for the following frame
According to the frame below, the goal is to determine the reactions of this frame in order to draw after the diagrams N, T and M.
The frame is asymmetric by reference at point C.
All reactions ...
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Does lead screw's thread have to be trapezoidal?
I want to move a small tool table/bed linearly, so I'm designing its mechanism. Fairly simple, it's going to have 2 rails and a lead screw.
Browsing the web I find that locally the shortest ...
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Is a beam is subject to axial load, does it mean that deformation is the same in each point?
If we look at a cross section at any point, stress will be the same $\sigma=F/A$ and the hooke law says that $\sigma=E*\epsilon$
It means that the deformation will be constant throughout the beam, ...
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Does same stress always produce same strain?
I am reading about pure bending from Beer Johnston's mechanics of materials. There, a prismatic member with a plane of symmetry was subjected to equal and opposite couples M and M' acting in that ...
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Compute deformation response history from ground motion
I'm reading a book of Anil. K. CHOPRA related to Structural Dynamics, I'm intending to obtain the deformation response spectrum from given ground motion. What I have here in hand is ug(t) ground ...
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How to calculate failure stress on a hollow pin loaded in shear
Calculating limit stress on a solid pin loaded in shear is straightforward, and there are several handy calculators which will do single shear and even double shear. However, everything I have found ...
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Solving for stiffness matrix numerically by a set of measurements
Is it in general possible when you have a mechanical structure (in this case I am referring to the structure in this post) and you want to determine the global stiffness matrix of this structure, to ...
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