# What is Stiffness: Definition and 172 Discussions

Stiffness is the extent to which an object resists deformation in response to an applied force.The complementary concept is flexibility or pliability: the more flexible an object is, the less stiff it is.

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1. ### Lagrange method problem: Multiple Spring-Mass System

4 I am working on problem c and I'm not sure if I'm doing it right, please can you help me understand if I am on the right lines? I want to get a better understanding of lagrange method problems Here is my working: I have labelled ##k_1,k_2,k_3,k_4, k_5## left to right Generalised...
2. ### Automotive Calculation of the reduced stiffness of a simple suspension

Hello, I have a problem with reducing a stiffness of a front suspension. Unfortunately I don't understand how to get the reduced stiffness on the right side in the picture. (k_f=k/cos^2E) Thanks in advance for your help. Many greetings, Semat10
3. ### JavaScript Physics engine with "angular stiffness" at joints

I have been experimenting with a minimal "toy" physics engine for JavaScript, called verlet.js but now I want to switch to a more versatile and feature rich engine. One feature I would like to use is the ability to assign a reference angle to a pair of segments (i.e. links, i.e. distance...
4. ### How to express ωₙ in terms of only mass (m) and stiffness (k)?

Summary: How to express ωₙ in terms of only mass (m) and stiffness (k)? I tried doing it with F=kx but it is out of my ability to simplify it to only m and k. Here is my approach:
5. ### The stiffness of an FEA model depends on the mesh resolution?

As is well known, the stiffness of an FEA model decreases with a refined mesh. What's the rigorous derivation of this?
6. ### ODE solver for second Order ODE with Stiffness and Mass Matrices

i am new to MATLAB and and as shown below I have a second order differential equation M*u''+K*u=F(t) where M is the mass matrix and K is the stifness matrix and u is the displacement. and i have to write a code for MATLAB using ODE45 to get a solution for u. there was not so much information on...
7. ### What size is the Global Stiffness Matrix in this Example?

does this Beam, composed of three elements and 4 nodes(considering lateral deflections and slopes) has an 8x8 global stifness matrix and if so is the global matrix calculated the same way as a 6x6 stifness matrix for the same kind of beam but only with two elements and 3 nodes
8. ### Stiffness by pressure calculations

Inflatable SUP boards, LEI kites, Inflatable kayaks, and so on get their stiffness by having two layers of airtight materials separated by pressurized air. And it gets stiffer the higher pressure you can contain, or by increasing the separation between the materials. The simplest way to look at...
9. ### Biophysics Q: Impact of stiffness (Young's modulus) on stress failure

Hi. I'm a physician trying to understand the micromechanics of lung injury due to overdistension. The basic idea is that overstretching of the plasma membrane of the lung epithelial cell causes "stress failure" --> i.e. plasma membrane rupture --> cell death. The concepts of stress, strain, and...
10. ### Structure adding rotational stiffness to a plate

I'm 3d-printing a part that is 110mm x 40mm (XY-plane). I have to keep it light weight, so I made it thin - 0.6mm (Z direction) and filled the surface with holes to remove as much weight as possible. Then I added a grid of 2,5 mm high "walls" in the XY directions to make it stiffer and a couple...
11. ### Trapping stiffness of optical tweezers

I read in some articles that the force in optical tweezers can be written as: F=kx, with no minus because the force will increase as the distance increased and the particle moves to the source..., This I can understand, but what I can not understand if I make integral (it is conservative force)...

13. ### Spring force after fixating with limited stiffness

Hi folks, I have an interesting problem here from the real world, it's a design i am working on. So I have an object that is pressed by an hydraulic press with 50kN, let's call it F_before. Then I drive in a jig to fixate it. But the part that holds the jig has a limited stiffness. Hence if I...
14. ### Does Increasing Mass Affect the Natural Frequency of Vibration?

My query here is, Suppose there is a 2 kg mass To oscillate it/vibrate it, it will take some force and it will have some natural frequency Now I increase the mass to 5 kg so to vibrate it, won't it take more force and so at the end, won't the natural frequency of the object increase? as its more...
15. ### Someone me understand the Stiffness of Materials

Summary:: I would appreciate it someone could help me as my mind is completely gone on this and I am struggling to get the correct answer. Hello, I am trying to use this formula to fill in the rest of the table and I expect to get an answer between 0-5 x10-11. However i am getting nowhere...
16. ### Stiffness Matrix Method: Symmetry vs Introducing a new node / joint

Hi, In the question outlined in the images (apologies for the poor quality of the scans), the chosen solution has opted to use a symmetry argument and proceed from there. Question is from "Structures: theory and analysis" by Williams & Todd My question is: How could we approach the same...
17. ### Spring stiffness and Heat Capacity (Equipartition of energy)

Here's a picture of what I tried. I was wondering if this is correct?
18. ### Stiffness Matrix For a Beam

hello i hope everyone doing well, I have problem in Stiffness Matrix For Beam element (2 nodes ) i have a beam element i want to get a stiffness matrix: we have beam element (2 nodes) node (1) : u1 horizontal displacement, v1 vertical displacement node (2): u2 horizontal displacement , v2...
19. ### Reducing the stiffness of a spring?

I have a spring which I am using to cushion a simple device, but it has proven to be too stiff for the purpose. Is there a way to reduce the stiffness of a spring, without making it brittle or malleable? I have access to ovens which can achieve 550°C, which can also quench in water or poly-oil...
20. ### What is the best resource for information on mechanical springs?

Hi, Is there a simple formula to calculate the lateral stiffness of a compression spring when both ends stay in parallel (see figure)?
21. ### Stiffness matrix for elastic materials

For an anisotropic material, is there any way to analytically determine the elements of the stiffness matrix? For orthotropic and isotropic materials, there are analytical expressions relating the stiffness matrix elements to the elastic modulus and poisson's ratio, but I do not believe this...
22. ### Stiffness matrix for a symmetric structure

Good day All While trying to solve the following exercice, I was stucked by a couple of issues for the first part in which we have to find the simplest configuration ( symmetry) according to my basic understanding Symmetry must be : geometry load support here I don t have the third...
23. ### Stiffness Matrix Issue: Get Help Now!

Good day All, while trying to solve this exercice I was puzzeld by the solution approach indeed, they use the symmetry of the structure, they have made a cut on the hinge where the force F is applied (the force F has been divided by 2 for the symmetry reason), and ONLY replace it with a...
24. ### Stiffness Stress Tensor Question

Homework Statement I am given c11, c12, and c44. What is poissons ratio ν and the E modulus E [100] for a single crystal for uniaxial strain in [100] (if Fe is isotropic)? ii) What is the anisotropy factor A? (iii) There is: sigma=[100 0 0; 0 100 0; 0 0 0]Mpa What is the transverse strain in...
25. ### I A perfectly stiff wheel cannot roll on a stiff floor?

I've been thinking about rolling motion, helped by @kuruman's excellent Insights article on the topic. A crucial insight from that article is that, when a wheel rolls along a flat surface, its axis of rotation is through the instantaneous point of contact with the ground, not through its axle...
26. ### B Clarifying Young's Modulus and Stiffness Equations for Cantilever Oscillation

Just want clarification on two equations. So basically, I want to calculate the time period T of the complete oscillation of a cantilever. I use this equation. Is E equal to young's modulus or is it equal to stiffness? If it is equal to stiffness, can I use this equation to calculate the...
27. ### How to increase the stiffness of a simple structure

Hello everybody, I am currently working on desinging a tool, and I would like to get your advice on how to increase it's stiffness. The tool will be used for correct positioning of a component. It consists of 2 parts : And
28. ### A block of mass m=0.2 kg, is pushed by a spring of stiffness k=300 N/m

I am currently taking a physics class and I'm studying for the final and I've been stuck on this problem and haven't been able to find help from the book nor help from online. The professor said the answer was .56m, but I've been trying formulas for about an hour now and haven't been getting...
29. ### Direct Stiffness Method for a distributed load

I'm working on a question which asks to determine the deflection, curvature, forces and moments of a simply supported beam with a distributed load. diagram shown in here http://imgur.com/a/wpI4kInitially, I've done the calculation with 1 plane beam element with 2 nodes. At L = 0 and L = 3. But...
30. ### Bending stiffness of circular bars

Which of the two is stiffer in bending? 1. A circular rod of diameter D and length L. 2. A circular rod of diameter d and length L, surrounded by a tube of inner diameter d, outer diameter D, and length L. The tube is not bonded and can freely move. It seems like an easy solution in that we...
31. ### Understanding Stiffness Modification and AA' Beams in Structural Engineering

Homework Statement I don't understand why the stiffness for span have extension pin stated from original stiffness ... According to online notes , for the far end pin / roller , the k is 3EI / L but not 3EI / 4L , is the notes wrong ? And i don't understand what is AA' beam , can someone...
32. ### Stiffness factor for member in beam

Homework Statement In this question , I don't understand why the KBC is 4EI / L ...Homework EquationsThe Attempt at a Solution I was told that for the far end pinned or roller supported , the K = 3EI / L , so shouldn't the KBC = 3EI / L.. Is the author wrong ? In the 3rd photo , we can see...
33. ### Is the Stiffness Calculation for Span Ends Incorrect in Online Notes?

Homework Statement I don't understand why the stiffness for span have extension pin stated from original stiffness ... Homework EquationsThe Attempt at a Solution According to online notes , for the far end pin / roller , the k is 3EI / L but not 3EI ***/ 4*** , is the notes wrong ?
34. ### Stiffness factor modification in beam

Homework Statement In this question , the author use only the left section of the beam for analysis ... How can we just consider a part of the beam for analysis ? We must consider the whole beam , right ? And find the KCD also . Second question , why there is no need to use carry over factor...
35. ### Help with spring stiffness calculation (k)

Hi I was given the following problem in my coursework: Homework Statement "A spring is initially compressed by 50mm when a steel ball of mass 2kg is released from just being in contact with the uncompressed spring. Determine the spring stiffness (k) of the spring." Homework Equations F = mg...
36. ### Upper Leg Muscles Wasting Due to Lower Leg Stiffness?

Is it possible that due to the less stretchness of th inner muscles of lower leg, the upper muscles waste? Being a student of physics, I don't know their names.
37. ### Direct Stiffness Method for Analyzing Tripod Frame with Equally Spaced Legs

Let's say you have part of frame contacting the ground, such as the feet on the base of the tripod. Assuming each leg is equally spaced around a center post, how would you go about analyzing this type of structure? I'm trying to teach myself how to use the stiffness method, but all the examples...
38. ### Stiffness Matrix of Frictionless Plate Support: Puzzling Differences

Hi all, In the attached photo, you can find a plate supported along the edge by "frictionless" support and I am trying to obtain the stiffness matrix using the node at the center. I wonder why the Kxx and Kyy (highlighted) are not equivalent or even near to each other, any suggestions?
39. ### How can I determine the overall stiffness matrix for a structure using Ansys?

Hi, I know that Ansys APDL can determine the stiffness matrix for any structure, I would like to know if I can determine the overall stiffness for this structure or not if yes how can I do this? thanks.
40. ### Effective stiffness of sandwich panels

Homework Statement Most sandwich panels are made up of two face sheets and a core. The core is often light, weak and contributes very little to the stiffness of the panel. This enables a very rough analysis to be made by assuming that the core is just air and that the cross‐section of the...
41. ### What is stiffness in a material

not a problem from anything just a question i have. problem: I know that youngs modulus (E) is known as stiffness. but when solving for elongation you can write e=FL/AE as F=se where s=AE/L and s is also known as stiffness. so I'm confused why is s and E known as stiffness when E is in the...
42. ### 2-DOF problem with unknown stiffness and velocity

Homework Statement I have a 2-DOF system, whereby I have one body that is grounded by a spring (body A), and a second body (body B) attached to the first by a spring and a viscous damper. For body A, I know the velocity and amplitude (before body B is added). I think I also have the stiffness...
43. ### What is the relationship between stiffness and Young Modulus?

What is the difference between stiffness and Young Modulus and how can you calculate the stiffness?
44. ### Automotive How to find "equivalent stiffness" of the suspension system?

Dude i have a problem to find the equivalent stiffness (k') and damping (c') of this equation ? thank youvery much physics forum
45. ### Rubber stiffness as a function of temperature?

I'm aware of the concept of rubber as an entropic spring and how increasing the temperature increases the modulus/stiffness of the rubber. I've seen the experiment of how heating a strip of rubber supporting a load will cause it to shorten. But also a rubber will transition from its glass-like...
46. ### Construction Materials Coursework: Stiffness Calculation Help

Stuck on a question in my Construction Materials coursework. Not asking for anyone to solve it for me but would be grateful if someone could point me in the right direction: As far as i was aware, stiffness = force/deflection, data which is not obtainable in a hypothetical circumstance.
47. ### Column analogy (Hardy Cross) - Carry Over Factor and stiffness

Hi all, 1. Homework Statement Book example: Determine using the column analogy method, the carry over factor from A to B and the stiffness at A for a propped cantilever. (Propped end is defined as A, and fixed end is defined as B) 2. Relevant principles 1. Moment at any point M = M_{s} -...
48. ### Good source homework problems for beam spring structures?

Hello there, In this semester I'm studying the vibrations course. In this course we get questions like calculating the total stiffness, set up differential equations and so on. The book that we use (Theory of Vibrations) has not been very useful, our exams give beam spring structures related...
49. ### Bending Stiffness: Derive Analytical Formula

Homework Statement Hi, can I please get some help with deriving the analytical formula for bending stiffness of a cantilevered tapered tube. Homework EquationsThe Attempt at a Solution
50. ### Increasing Cantilever Beam Stiffness

Is it possible to create a cantilever beam with constant or increasing stiffness. I've been experimenting with several different shapes and profiles, and have not had any luck. I know that there are shapes with constant stress throughout, but I'm hoping to find a shape with constant or...