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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Modeling composite material fibers orientation in a FEA

I am looking for guidance for analyzing composite materials that are reinforced by fibers of some sort. A good mental model would be bars of steel in concrete. The concrete will have its own physics ...
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Why doesn't the Stress Power in the theorem of the expended mechanical power contribute to the kinetic energy?

The following is the formula of the expended mechanical power: $P(t)$ $=$ $\frac{d}{dt}$ $\int \frac{1}{2} \rho\ v^2 dV$ $+$ $\int \sigma \colon d\ dV$ where $P(t)$ is the mechanical power entering ...
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24 views

Can FSI analysis be linear on the solid part? [closed]

Is the FSI analysis always considered Nonlinear or the solid part analysis can be linear too?
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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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1answer
73 views

Infinitesimal Strain Tensor in Cylindrical Coordinates

How can I obtain the below formulas of infinitesimal strain in cylindrical coordinates using matrix calculation given the first formula? I find it hard to study them because I still don't know how to ...
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Sprocket Angular Velocity [duplicate]

I have a question please that I need help on. Consider the chain that is draped over the sprocket with mass moment of inertia of 0.005kgm^2 about central axis. If 4kg block is released from rest from ...
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How much is the braking torque of this belt brake?

I just thought of a mechanism that has a belt brake, but I cannot calculate the braking torque. On the picture, the middle black shaft is stationary, and the blue is rotating with ω1 speed. The green ...
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2answers
37 views

How much weight can a cardboard of size $n \times m$ hold? [closed]

I am interested in knowing how much weight a piece of cardboard can hold in proportion to it's size. Suppose we have independent variables $x$ and $y$ corresponding to length and width and that these ...
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1answer
48 views

Stretch in Infinitesimal strain theory

In the picture above we have the expression of stretch with respect to strain tensor, but in case of infinitesimal strain theory, we take stretch equal to 1+T.E.T I don't understand why by taking ...
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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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1answer
32 views

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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Confusion in the Lagrangian description of Material Surface in Continuum Mechanics

In Lagrangian or Material description, the physical properties are described in terms of the material coordinates and time. It focuses on what is occurring at a fixed material point (or particle) ...
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Rearranging to find Vmax

I have a solution to a problem on the mechanics of materials. For the last step to find the deflection Vmax I am not sure how equation (15) was simplified to get the answer shown below:
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1answer
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Want to simulate a mechanism with spring in it for forces acting in different direction (Kinematics). How to do it using solidworks or ANSYS? [closed]

Thought of using motion study in Solidworks but not able to account for forces at the different axis in it here is the image to better understand it. There hasn't been any progress with the ...
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1answer
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Why is the displacement gradient tensor equal to zero when the motion is pure shifting?

In this video at 6:15 https://www.youtube.com/watch?v=ZO8P2iiQGDc By calculation, it is clear that displacement gradient tensor equal to zero when the motion is pure shifting (no change in shape). ...
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Resultant of coplanar forces

I have a question that goes thus. At what angle $\theta$ must the $500N$ force be applied in order that the resultant $R = 1000N$. For this condition what will.ne the angle $\beta$ between $R$ and ...
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1answer
60 views

How is it possible for trajectory and streamline to coincide in case of stationary velocity field?

In continuum mechanics, the definition of trajectory or pathline is the locus of the positions occupied by a given particle in space throughout time. And streamlines are a family of curves which for ...
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35 views

What is the angle of twist in end point A?

Can anyone please explain this question to me? I am okay with answering a gear assembly with 2 gears at a time. But the third one here is confusing me.
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1answer
37 views

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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Help in synthesizing cam profile (oscillating cam and oscillating follower)

I am using Matlab to plot contour of the cam. So far, I understand how to use angular displacement relation between cam and follower to get the profile, pressure angle, torques etc. What I aim to do ...
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1answer
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I need something similar to a 3“ to 5” curtain tension rod to fix my popping air ducts

The air ducts in my house have a couple of places where they make popping sounds as they expand while heating, one of the loudest ones is annoyingly in my bedroom. I know by pressing around where I ...
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16 views

Stress Tensor components

Given an equivalent stress vector(or Traction vector) in a plane stress state, how can one determine the 3 components of the 2*2 Tensor matrix, i.e. sigma_x, sigma_y and tau_xy?
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Stress Transformations

In plane stress state: How can one comment about the state of stress for the given condition? I am not sure but I guess that we can use the principle of superposition. Though I do not know how can I ...
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Definition of Mass in Multiple Mass Oscillators

In an exam on seismics and earthquake proof design I had a couple of days ago, there was a question on multiple mass oscillators in the form of a simply supported beam of length $L$, stiffness $EI$ ...
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Why do I see stresses on the fixed support face of a solid body in FEA?

Below, I have shared pictures of a simple model in FEA. As it can be seen that the face onto which the fixed support is applied, there exists Von-Mises stresses. I cannot comprehend why. Since the ...
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Transformation of 8mm straight motion to 210 degree motion

Everyone. I want to make the transformation form Straight motion to Rotational motion ,like [this].1 So I made . But it did not work. Probably, this was mistake of Groove size on spiral groove. But ...
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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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72 views

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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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 equations of motion, $...
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1answer
62 views

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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45 views

Calculate the residual stresses in the bars and the residual displacement of the $ C $ point when the $ P $ force is removed

Consider the rigid bar $ ABC $ linked to two bars, $ AD $ and $ BF $, as shown in the figure. All bars are made of mild steel which is admitted to be an elastoplastic material ($ E $ = 210 GPa, $ \...
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Quantifying the amount of structural/hysteretic vibrational damping that occurs in proportion to deformation? (ie. Based on how “bent” something is?)

Three different conceptual types of vibrational damping forces are described here: Viscous: $f(t) = -c \cdot v$ Coulomb: $f(t) = -c \cdot \text{sgn}(v)$ Structural: $f(t) = -c \cdot |x| \cdot \text{...
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86 views

Determine the value of the largest $ P $ load that can be suspended at the $ E $ point without the vertical displacement at that point exceed 0.25 mm

The figure represents a rigid bar $ BCE $ connected to two steel ties $ AB $ and $ CD $ ($ E $ = 200 GPa). The rods are connected by joints at the ends and have a uniform cross section of 6 $ \times $ ...
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1answer
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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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Can anyone help me with the concept of bearing stresses in steel reinforcement in Reinforced Concrete?

When there is tension reinforcement(steel) embedded in concrete, does it not also undergo bearing stresses on account of the weight of the concrete and other forces which are acting above the steel? ...
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1answer
84 views

How can I decrease strip tension with bridle rolls in tension leveller? How can I find total elongation after the strip exits initial bridle rolls?

I'm working on a tension leveller design which consists of 3 main sections. These are Input Bridle Rolls Zone: Increase the strip tension coming out of the decoiler. Leveller Zone: Strip goes through ...
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2answers
60 views

maximum allowed load [closed]

I have the following problem E= 210 MPa d = 40 mm n = 20 y = 1.5 a =1 calculate the maximum allowed load for the system I am confused on how to solve the problem, I really need advice.
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how to find the tension matrix knowing the extensions

At a point $ P $ on the surface of a body, the rosette of 45 gauges indicated in the Figure is glued, whose readings are $\varepsilon_1 = 2 \times 10^{-6}$ , $\varepsilon_2 = 1 \times 10^{-6}$ e $\...
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Determine two values of σ22 for which the maximum shear stress is 80 MPa

Determine two values of $\sigma_{22}$ for which the maximum shear stress is 80 MPa i know that \begin{equation} \sigma_{ij} = [\sigma]^\top = \begin{bmatrix} \sigma_{11} & \tau_{21} & \tau_{31}...
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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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Choice for HEAVY blacksmith table

I have an old 7,000 lb. blacksmith table (I had it weighed at truck stop). Similar to the one this man has: Sorry for the size of the pic. I need to lift one end the way he is doing and I have a farm ...
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1answer
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What is the steel used for CHC DIN912 class 12.9 exagonal bolt?

I would like to know which steel is used for CHC class 12.9 bolt DIN912 (i am looking for the young modulous & poisson ratio of the material). Thanks a lot. Alexandre
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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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2answers
69 views

How can I find deflection in a member that doesn't have a constant area moment of inertia?

I'm trying to calculate the maximum deflection in a simply supported member with a uniformly distributed load. The trouble is this member does not have a constant area moment of inertia. I've drawn a ...
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1answer
97 views

transformation matrix from the original reference to the main reference

Consider the state of tension in the neighborhood of the point $ P $ represented in the Figure. Determine the principal directions of the stress state in $P$ and write the transformation matrix from ...
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Determine the range of τxz values for which the maximum tangential stress is less than or equal to 60 MPa

Consider the state of tension indicated in the Figure. Determine the range of τxz values for which the maximum tangential stress is less than or equal to 60 MPa. I did σ(med)=(60+0)/2 = 30 To find ...
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How to plot bending moment diagram from shear force diagram

With conventions that I adopted shown below I drew roughly the shear force and bending moment diagram of a simply supported beam with concentrated load at the middle. Now while drawing I drew both ...
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How can we model viscoplastic softening using slider, dashpot & springs?

I am working on a brittle material which shows elastic behaviour followed by viscoplastic softening & hardening in the end (in compression with accumulating damage). I am not able to think of an ...
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1answer
86 views

Stress vector that acts on the plane

A flat plate with dimensions 110x220 mm is subject to the indicated stresses. Assume that $\sigma_{zz} = 120\ MPa$. Determine the stress vector that acts on the plane defined by the z axis and the ...