# Questions tagged [solid-mechanics]

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### Rotation Matrix for a Stress Tensor Matrix

In my engineering mechanics course, I came across the following rotation matrix, for a stress tensor, for a counter-clockwise rotation. However, this is completely different, actually a transpose of ...
25 views

### Torsional rigidity of a composite shaft in parallel

Consider the following composite shaft which consists of 3 different materials with modulus of rigidity of $G_1$, $G_2$ and $G_3$. Shaft 1 has length 2L, and shafts 2 and 3, L. Assume they are all '...
24 views

### how to determine the direction of support reactions in a truss?

Hi, I am not sure how to determine the direction of support reactions at point A and K. I know point A has a pin support, therefore, it can take in horizontal and vertical loads and point K has a ...
28 views

### Determining the angle theta at the Mohr's Circle

I'm having trouble about deciding the initial angle theta before drawing the Mohr's circle. From what I've learned from the lecture, I need to draw a normal line of indicated plane and find the angle ...
41 views

### Ideal design for a long fruit plucking pole

I need to design a long (6-7m) pole for plucking fruits from tall trees. The following are the requirements: The pole material needs to be as light as possible. The pole should not be flexible ...
47 views

### Strain energy, Conservative force and Potential energy

What I know: In general, the work done by a conservative force $F$ is equal to the negative change in a potential energy. $$\int_1 ^2F.ds = - (U_2 - U_1)$$ A potential energy is always associated ...
47 views

### What is the difference between an alloy and a metamaterial?

Metamaterials are carefully structured materials — often consisting of periodically arranged building blocks — that exhibit properties and functionalities that differ from and surpass those of their ...
6k views

### 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 ...
76 views

### Work done by a force in a deformable body

Consider a deformable body that is acted upon by several forces at different points of application. Under these forces, the body remains at rest but deforms and the particles have some displacement. ...
1 vote
50 views

### Constant tension...does angle between rollers matter?

Thank you in advance to anyone with time to take a look at my question here. For anyone interested, this is a question in regards to an open source film scanner project, which can be found here: https:...
95 views

### 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 ...
32 views

### Derivation of deformation equation given thermal expansion

I'm working on a thermal expansion problem out of Beer & Johnston's Mechanics of Materials and I'm a bit confused by the underlying rationale of one of the steps in the solution process. In the ...
18 views

### Viscoelastic modeling, what is wrong with my Boltzmann Superposition integral?

In a similar setup to many Micro-Pipette Aspiration experiments, I have a ramp-and-hold aspiration, and calculate the resulting elevation using the Boltzmann hereditary integral. My aim is to fit the ...
41 views

### Stress in a L-shaped Beam due to Thermal Expansion

A L-shaped frame $ABC$ (right angle at $B$) consisting of beams $AB$ and $BC$ are fixed at ends $A$ and $C$ to rigid walls. Find the tensile stress at $A$ when the temperature of the frame is raised ...
1 vote
22 views

### should the hachures in moment and shear diagram be vertical?

when we plot the shear or moment diagram we add hachures to the area created with these diagrams , in most cases we see vertical hachures, is it represent the internal forces? or its just used to ...
60 views

### Why were handcuffs ever made with a chain between them?

I've noticed that modern handcuffs are always attached directly to each other, without any "chain" of any length in between. I guess I can understand why that make them safer and more robust....
27 views

### Relationship between shear moduli in an orthotropic material

I'm confused what the relationship between each of the shear moduli are in an orthotropic material. From what I understand, there are 3 independant major shear moduli, G12, G13, and G23. They each ...
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### Why is the fluidization pressure drop profile different when this one is measured while increasing and decreasing fluid flows?

why is it that when measuring pressure drop across a solid particle bed at different fluid flows the pressure drop profile looks different? When you measure pressure drop while increasing fluid flow, ...
68 views

### How can I find stiffness of a steel coil spring used in dump trucks?

How can I find stiffness of a steel coil spring used in dump trucks? Here is the data of the question. Length of spring unloaded = 220mm Outer Diameter = 27mm Inner Diameter = 15mm Wire Diameter = 6mm ...
204 views

### How to calculate press load for an interference fit with no friction coefficient between the materials (shaft & hub)

Press-fit load calculation always takes friction into consideration and gives you the load expression as follows, $$F = µ\cdot PA$$ where µ is the friction coefficient, P (Interference Pressure) is ...
66 views

### Is there a way to solve this complex statics problem algebraically?

This problem can be solve in 2 ways either I solve it with vectors which would be relatively painful and more time consuming and the other faster way is algebraically but I faced a problem when trying ...
64 views

### How will the reaction moment on the support be distributed in terms of forces in this model?

Consider a rectangular cross sectional solid beam, fixed at one end and a uniform shear force applied to the other end. Below shows the side view for this beam. Now, I change the support area as ...
45 views

### Question about cam follower design

It's always said that jerk function should be smooth to avoid undesired vibrations. What exactly is the vibration in a cam follower mechanism and why is it important to avoid it?
1 vote
81 views

### Is Smith Diagram and Modified Goodman Diagram the same? And how does one construct it?

I am confused about the names. Moreover, I haven't found any textbook which attempts to show step-by-step construction of these diagrams. I would be happy if anyone pointed to some textbooks or even ...
48 views

### What is meant by Solid Mesh and Surface Mesh? [closed]

Solid Mesh vs Surface Mesh, which method should I choose in simulation studies. What is the geometry behind these meshes. Which mesh gives accurate results?
317 views

### How many more degrees of tilt can the Millennium Tower in San Francisco withstand before it becomes structurally unsound? [closed]

How many more degrees of tilt can the Millennium Tower in San Francisco withstand before it becomes structurally compromised/unsound? "...An examination in 2016 showed the building had sunk 16 ...
1 vote
2k views

### 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 ...
998 views

### 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 ...
1 vote
54 views

### Can we use the Flexural formula and the Beam theories for bodies made up of Composite materials?

Below shows a link for the derivation of Flexural formula. Derivation of Flexural formula In this above link, there are a few assumptions made to reach to its final form. They are shown below. By ...
1 vote
49 views

### Bending stress wave resulting from a lateral impact on a beam

I want to approximate a bending stress wave resulting from a lateral impact on a beam which is on one end fixed. According to Roarks 16.3-3 I can estimate a compressive stress wave from one mass ...
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### Holzapfel-Gasser-Ogden (HGO) model

Can Holzapfel-Gasser-Ogden (HGO) model be applied to solid porous materials such as rocks, concrete and etc. as well? If yes, would you please introduce a reference. If not, is there any modified ...
45 views

### Can the general Flexural formula be used in the case of transverse loading of a beam?

The general derivation of the Flexural formula uses the pure bending case, where the distance from a curved section to the neutral axis is assumed to be constant even after bending, denoted by y. The ...
18 views

### Clad Cylinder Thermal Stress Analysis

How can one determine the thermal stress between the clad and the substrate on a clad cylinder? How can one determine the thermal stress on a clad plane? Can it be shown that if the radius is ...
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### Which of these two cases will have the most friction?

I have a structure colored in blue which we are looking directly downwards on (birdsview). Its high up in the air, and the only thing keeping it from falling down is the friction surface (red) between ...
89 views

### Beam with width tending to zero

Suppose a cantilever beam (of rectangular cross-section) subjected to vertical transverse shear load at free end. If I consider any arbitrary cross-section then both bending and shear stress will be ...
156 views

### 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 ...
96 views

### 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 ...
585 views

### 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 ...
22 views

### How to choose contravariant or covariant bases?

I completed an introductory course on continuum mechanics, but we did not delve into curvilinear coordinates with CM. However, when I read some publications I see the stress-strain relationship is ...
18 views

### Stress divergence of elastically deformed body is not zero

TL;DR According to the analytical solution (link) for a deflection of a cantilever beam $\sigma_{xx} = - \frac{P xy}{I}$, $\sigma_{yy} = 0$ and $\sigma_{xy} = -\frac{P}{2I}(\frac{D^2}{4} - y^2)$ and ...
80 views

### In FEM, what is the difference between a single element with a quadratic shape function and two elements with linear shape functions?

Using Finite Element Analysis to obtain a Weak form of a PDE, what is the difference between the two cases: A single element with a quadratic shape function Two elements with linear shape functions. ...
1 vote
104 views

### What is the difference between max shear stress at neutral axis in bending and max shear stress from Mohr's Circle?

The maximum shear stress which we get from the equation: $\frac{VQ}{It}$ (for instance, the maximum shear stress at the neutral axis for a rectangular beam cross section, fixed at one end and ...
1 vote
32 views

### Strain gauge measurement using NI 9944

I am trying to measure the strain on a part using a strain gauge. The gauge is a 120 $\Omega$ strain gauge from HBM. I am using National Instruments (NI) hardware and LabVIEW software to capture the ...
608 views

### 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 ...
21 views

### Connection between strain energy density and energy due to a moment

Can the strain energy density (volumetric density) always be written as $\frac{1}{2}\sigma\varepsilon$ as long as the object is subject to just axial loads and moments (neglecting the work done by ...
1 vote
106 views

### 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 ...
80 views

### Why am I seeing a moment reaction at the supports for these beams in FEM?

Please observe the Finite Element model below, in ANSYS WorkBench, (Remote force behavior = Deformable). Also, please take a lot at the force and moment reactions at the fixed supports. I couldn't ...
1 vote
25 views

### equivalent Hertzian contact pair for arbitrarily shaped bodies in 2D [closed]

I am a bit new to this field here. I am trying to determine the contact stress between two arbitrarily shaped bodies that are indenting into each other (see attached image). I would like to solve ...