Stiffness Definition and 174 Threads

Hi, For an undamped mass, spring system subject to a harmonic force, the equation is: ma+kx=Fsin(ωt) where a=d^2/dx^2 After solving the diff eqns, the steady state amplitude is: X=(F/m)/(ω^2-ω0^2) where ω is the frequency and ω0 is the natural frequency =sqrt(k/m) according to the...

My main question is why we derive the structure matrix for a beam like the attached first picture; we assume the beam on the left on point B has no deflection? While i check this by computer analsysis program and it has an effect. Please explain in details The second question is the...

Guys when i study earthquake , they told me that the column stiffness is 12EI/L3 if column is fixed -fixed and 3EI/L3 if column is pin -fixed, so how they get this, i try to study stiffness Matrix and it gives you big matrix for frames not Only one factor like 12EI/L3 please explain

Hey guys I am looking for the solution to replace the spring in MDOF model with wind stiffness or air stiffness if to build a MDOF model of wind. What I have now is only a wind speed data matrix. Anyone can provide some equations of calculating wind stiffness and some clues maybe...

I am currently working for a Touring Car Team . I have modified the front suspension geometry . Made the roll moment lesser and increased the Roll stiffness . Driver complained that the steering effort has increased considerably in the corners . 1.How does increased roll stiffness increase...

Hi, I have forgotten quite a bit of my vibration studies, so I have a fairly basic question. Essentially, when you want to find the natural frequency of a single dof system, you use ω=√k/m. However, does anyone know a general procedure (not problem-specific) for finding "k" that is applicable to...

I have gone through Beam Element analysis in several books on FEA. 80% of books have a particular Stiffness matrix, while a very small number of books have a matrix which is subtly different in sign. http://www.flickr.com/photos/66943862@N06/7195680680/in/photostream/lightbox Most books have...

Homework Statement You are tasked to reduce the vibrations of of an old air conditioning unit through the structure of a building. To do this you intend to mount the fan unit on 4 free-standing spring isolators with a non skid base. By choosing the appropriate springs and configuration you...

Homework Statement I'm unable to calculate the stiffness of the spring. Once, i get the stiffness i'd like to calculate the load required for the defined deflection. Homework Equations - The Attempt at a Solution -

Homework Statement I'm trying to figure out the mass and stiffness matrices for the following system: Homework Equations J1 = 3600 kg-m^2 J2 = 200 kg-m^2 J3 = 800 kg-m^2 J4 = 4800 kg-m^2 G (shear mod) = 8e10 Pa The Attempt at a Solution I've tried this setup: M = |J1 0...

Homework Statement So I'm doing a string/wire telephone experiment where I'm using a signal generator to vibrate a wire at a certain input frequency. I am then taking results down for the Amplitude output. I'm not quite sure on the relationship between Stiffness constant K and Amplitude. I've...

Dear all, I have written a code for structural analysis using the finite element method. For some reason, I directly started with 3D elements ( hexahedron). I used to believe that the code was fine but recently i realized that the results ( deformation, natural frequency,..) strongly depend...

This is not a HW question, but a question that I need help solving. I am having an argument with a co-worker about the solution. There is a 4ft sq sheet of plywood with an 18" wide rubber band stretched across it. To measure the spring constant (stiffness) of the rubber band a 6" diameter...

Stiffness of a single interatomic "spring"? One mole of iron (6 x 10^23 atoms) has a mass of 56 grams, and its density is 7.87 grams per cubic centimeter, so the center-to-center distance between atoms is 2.28 x 10^-10 m. You have a long thin bar of iron, 2.8 m long, with a square cross...

Hi community member, Regarding the book that I'm reading original writer has used Ni = ai + bi*x + ci*y shape function for the formulation of stiffness matrix for thick triangular plates. The writer has not mentioned in the article that the resulting stiffness matrix is required to be...

I have a problem in the understanding of stiffness. For a simple cylinder with force acting axially, the definition of stiffness works ie Force per unit displacement. but what happens if the cylinder is bent, or even better a plate clamped on the edges with a UDL? In this case displacement would...

hi all, Actually I'm looking for little help and kinda confirmation, in order to verify that I understood the logic of construing the stiffness matrix. I got the logic of how to construct the stiff matrix for bending and membranes to some level, although FEM books suggests to simply combine...

hi, I'm studying the book for elasticity theory and I stuck at one of the equation in that book, the stiffness matrix for elements(thin or thick plate) in bending is given in that form ke= t∫∫BT*Db*B*det(J)dζdη+∫∫BT*Ds*B*det(J)dζdη B is the strain matrix(5x12) where the inner...

Folks, See attached. I wish to calculate the tilt stiffness as a function of some linear stiffness. My attempt is on the RHS of FBD and there is somebody elses attempt on the LHS. I am not sure if it is right. I have 2 queries 1) My attempt on the RHS I wrote the expression of f in...

Folks, See attached. I wish to calculate the tilt stiffness as a function of some linear stiffness. My attempt is on the RHS of FBD and there is somebody elses attempt on the LHS. I am not sure if it is right. I have 2 queries 1) My attempt on the RHS I wrote the expression of f in...

A 73 kg trampoline artist jumps vertcally upward from the top of a platform with a speed of 4.8 m/s. a) What is his speed as he lands on the trampoline, 2.6 m below his jump off point? Express your answer to 2 significant figures. = 8.6 m/s (already figured out this to be the correct...

I am replacing an exisitng solid rod with a new rod with a rod made from a different material and a different cross section. The new material has a MOE that varies with skin depth which is making it hard for me to develop an expression for stiffness (EI). The new rod has a hollow...

So say I have a steel pipe under a torque and an axial load. I want to know whether the axial load has any effect on the twist due to torque. Have one calculation which (perhaps falsely) assumes the pipe is made of lots of axially running "wires" and calculates the torque due to this axial...

http://www.flickr.com/photos/53948823@N08/6193375731/ I need to solve this problem but with member 2 as L+e instead of L, and omit the load.. Since I only see one degree of freedom, i don't know how to set up the matrix to solve for the 3 forces. I have K11 = EA/L + (EA/(L+e))cos2(30) +...

Hi all, I am trying to understand the concept of equivalent stiffness of a beam. As I see it, the equivalent stiffness is the stiffness of a linear spring that would deflect the same amount under the same load. For a cantilever beam with a load P and a deflection \delta at the free end, if we...

Hi guys, I must simulate with simulink an air spring, connected to a device. In many book is present this non linear formula: k(h)=-(n*P0*Ae*h0^n)/(h^(n+1)) Where: P0 is the air pressure at the equilibrium condition h0 is the spring heigth at the equilibrion condition Ae=F/P0 is the...

Hello can someone please tell me the difference between stiffness and hardness and between strength and toughness? thanks

Hello guys How can I calculate the following stiffness of the springs/suspensions in the case of inclined suspension (angle between suspension and axle)? I know that the lateral separation of the springs causes them to develop a roll resisting moment proporcional to the difference roll...

hi.. This is abdul I am carrying a impact of sphere on a composite laminated plate. i wanted to calculate the contact force when sphere impacts the plate.. or can anyone help me how to get the stiffness of plate.. or deflections in plate.. with respect to time Thanking you Your help will...

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...

ok i loaded a composite laminate beam across the centre of a 1.44meter span with 415N load. This deflected the beam to a distance of 0.05m (5cm). Im having trouble calculating the stiffness from this. The composite laminate is 5mm of wood in a glass fiber sandwich with both the top and bottom...

So, I am trying to assemble the Stiffness Matrix in my Finite Element Analysis course (Structures) and I keep coming out with a stiffness matrix that is not symmetric. I learned that for any neutrally stable structure, the stiffness matrix must be symmetric. Are there special cases that I am...

Homework Statement In an earlier chapter you calculated the stiffness of the interatomic "spring" (chemical bond) between atoms in a block of lead to be 5 N/m. Since in our model each atom is connected to two springs, each half the length of the interatomic bond, the effective "interatomic...

hi i need to calculate the torsional stiffness of a sample, the data is in the excel file. To work it out it = 1/samplek= 1/totalk - 1/machinek the machine k was given as 42800NM/radian the total k is the slope of the line which comes to y=658x what i don't get is what am i meant to...

Hello. Supose that we have a cantilever beam. For a small force P applied at the free side of the beam, we can find an expression for the maximum deflection: \delta=\frac{P l^3}{3 E I} If we want to use this beam as a string, we can find its equivalent stiffnes noting that P=K_{eq} \delta, so...

What does the spring constant mean for the overall "stiffness" of a spring? Does a larger spring constant mean the spring would be more difficult to compress or stretch? I know that Hooke's law states that F=-kx, and that the units of k are in N/m, I just want to know what the spring constant means.

what is the spring stiffness?!??! In outer space a rock of mass 4 kg is attached to a long spring and swung at constant speed in a circle of radius 6 m. The spring exerts a force of constant magnitude 720 N. What is the speed of the rock? i found the speed it is 32.8 m/s part 2: The...

What is the Spring Stiffness? [b]1. One mole of iron (6.02x10^23 atoms) has a mass of 56 grams, and its density is 7.87 grams per cubic centimeter. You have a long thin bar of iron, 2.4 m long, with a square cross section, 0.15 cm on a side. You hang the rod vertically and attach a 234 kg mass...

Hi all, I'm trying to design an arch for a project (will be about 4" long). This arch will be experiencing a load on its vertex, and I need to make sure that the arch will not deform very much. What is a good way to model the stiffness of an arch like this? As far as I know, there is no...

Hi All, Sorry for the cross post, I had an earlier version of this in Classical Physics which has errors. Please disregard. Problem Description: The drawing shows an adapter to secure a container to arms which connect to an off road moving dolly (not shown). A 6x6 beam has two arms (6"...

Problem Description: The drawing shows an adapter to secure a container to arms which connect to a moving dolly (not shown). A 6x6 beam has two arms welded to the ends that support the container at the sides and two opposing arms (4" deep and 8" wide) offset 2' toward the center that connect...

So I was doing some FE work (w/ NASTRAN) to determine the stiffness in all 6 DOF of a model bolted to another model. To characterize the bolted interfaces I attached surface nodes within the bolt frustums to rigid body elements (RBE2). Then, these RBE2s were connected with a directional...

Hi all! Im stuck with a bit of a problem. I have a wedge shaped petal valve which I need to find the spring stiffness k and hence the natural frequency of vibration for. In all the texts I've looked up so far, the equations have always assumed the beam is of constant cross section or has a...

How is stiffness affected by potential?

2. The equation you will be using is given by T = kx. Please refer to chapter 17 in the book for a reminder. I require you to design an experiment to calculate the stiffness constant k for the bungee rope I have given you. In the report you should consider the following points a. What type...

Homework Statement Can somebody please explain me: What does it mean that Longitudinal Stiffness (EA) is equal to infinity? What does it change if for some members of a structure "EA = infinity", and for other members "EA = finite number". Homework Equations I know that we use longitudinal...

Inter-atomic force in a Hydrogen molecule -- finding "spring" stiffness Homework Statement At about 2000 K the heat capacity (at constant volume =) increases to (7/2)k per molecule due to contributions from vibrational energy states. Use these observations to estimate the stiffness of the...

Homework Statement One mole of iron (6 *10^23 atoms) has a mass of 56 grams, and its density is 7.87 grams per cubic centimeter, so the center-to-center distance between atoms is 2.28 *10-10 m. You have a long thin bar of iron, 2.9 m long, with a square cross section, 0.05 cm on a side...

Homework Statement A spring has a relaxed length of 6 cm and a stiffness of 150 N/m. How much work must you do to change its length from 8 cm to 12 cm? Homework Equations 1/2Ks,f - 1/2Ks,i The Attempt at a Solution 1/2 Ks,f^2 - 1/2 Ks,i ^2 1/2 (150)(0.06m)^2 -...

I am having trouble forming the Global Stiffness Matrix for a planar truss. Does anyone know of any good online resources to help me with this? I've found a few, but haven't been much help.