In applied mechanics, bending (also known as flexure) characterizes the behavior of a slender structural element subjected to an external load applied perpendicularly to a longitudinal axis of the element.
The structural element is assumed to be such that at least one of its dimensions is a small fraction, typically 1/10 or less, of the other two. When the length is considerably longer than the width and the thickness, the element is called a beam. For example, a closet rod sagging under the weight of clothes on clothes hangers is an example of a beam experiencing bending. On the other hand, a shell is a structure of any geometric form where the length and the width are of the same order of magnitude but the thickness of the structure (known as the 'wall') is considerably smaller. A large diameter, but thin-walled, short tube supported at its ends and loaded laterally is an example of a shell experiencing bending.
In the absence of a qualifier, the term bending is ambiguous because bending can occur locally in all objects. Therefore, to make the usage of the term more precise, engineers refer to a specific object such as; the bending of rods, the bending of beams, the bending of plates, the bending of shells and so on.
I'm doing some modeling of a bending magnet in FEMM, to use as a magnetic spectrometer, and came across the following equation:
with the setup of the magnetic spectrometer similar to the following figure:
At first I modeled a hard edge scenario in a 2D cross section, where no fringe fields had...
I found the internal force Vxy 25 +6 =31kn. , bending moment Mmin -qb2/2 , M min- 14 kNm. delta =M/W I can't find Mmax and tau= V/As. So I need help to find Mmax and As wall area, how to find.
I need to make a set of dies to roll form a 1" wide strip of 5052-H32 0.063" aluminum for a home project. The bend radius is 1T (0.063") and I want to bend it to 90 degrees. My understanding is that this type of aluminum is a bit springy. So if someone could give an estimate on how much spring...
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I'd like to calculate the maximum deflection of a simply supported beam with spring support in the middle and UDL (uniformly distributed load) acting on the whole beam:
Here's my derivation, starting from the known formula for maximum deflection of a simply supported beam with UDL and no...
Do gussets perform well in cantilever bending when horizontally oriented, as opposed to vertically oriented? I assume vertical orientation performs well in bending, in which you can calculate the area moment of inertia by adding that of the gusset cross sections individually, and the joint helps...
As you can see from the picture, the cross section to analyze is idealized and the boom areas resulting from this are given.
For POINT A) all I did was:
for determining the shear forces, integrating the shear flows over the sides to compute the vertical and horizontal contribution of each side...
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Negative Gust (what is the sign of Gust Load Factor , is it for example +6.3 or -6.3). And does that mean the tips of the wings is going up or down ( if going up does that termed in "English" as Up-Bending of Wing. ?Also, in this case (Negative Gust), if we call inner flange of the top...
In engineering statics I've learned the concept of bending moment, which in some way indicates an applied load that tends to bend the object, and it seems that it can move around freely in the reference frame. (I understand moment in engineering is not quite the same concept as torque in physics...
TL;DR Summary: Finding maximum bending moment on a boom
I am trying to solve the problem stated in the picture below.
The answers are given.
I've manage to find the Normal and Shear Forces but I'm stuck at the bending moment.
According to my analysis the maximum bending moment is +7208,1...
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In order to make a metal preframe for a French window as an entrance door, I began to estimate the possibility of building it in rectangular steel tubes of 100 x 50 x 3 mm, laid independently of the walls that could not accept such a load because it was timber framed. The preframe will...
The equivalence principle tels us that we cannot distinguish between gravity and an accelleration. using that fact one can reconstruct the bending of light along the sun, but only half of it results from the equivalence principle together with the gravitational field around the sun. Is it...
How can I find the maximum bending moment and maximum deflection for a spring?
It would be very helpful if you could explain the specific procedure and formula in an easy-to-understand manner.
that's all, thank you very much.
Greetings!
As you could see the moment try to make beam to rotate in the support plane with the wall which mean for me this moment is on the Z direction but the longitudinal axis is the X direction and I know that for a moment to be torsion it needs to be in a longitudinal direction, but the...
Summary:: Calculate the deformation on a rod/axle/pipe due to a distributed load.
I’m manually trying to calculate the deformation on a rod/axle/pipe due to a distributed load. The rod has an outer diameter of 62mm and an inner diameter of 50, is 170mm long, made from a material with an...
Hello,
I have an flexure where the force is applied asymmetrical, I just can't visualize why their should be a bending moment instead of an bending force? How can I distinguish those? Thanks!
Some more details on the system are that L1 is very long (close to 100ft) and L2 is close to 30ft (the vertical pipes). The piping is all schedule 40 1/2" OD. Moment of inertia is roughly 10^-8. Components are about 2kg each. The distance of the pipes horizontally is small (around 2ft). Pressure...
How come in the lewis bending equation for spur gear tooth does the lewis form factor depend on x? x being the vertical distance measured from the triangle that is formed from the base t and fillet a. I know that you can express the height h and width t in terms of x such that x= t^2/4h, but why?
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I'm trying to calculate the deflection of a leaf spring. I've found several formulas but the one I'm currently using looks like this: $$f=k \frac{F L^{3}}{6EI}$$ where: ##k## - coefficient depending on the way leaves change their shape in the width direction (in my case it's ##1## because...
Hello everyone, I hope you can give me hand with what I will present.
I have a beam with cross-section shown below.
I considered a simple linear hardening model for predicting the stress and strain developed by bending the beam on the radius ##R_0## around the y-axis, where:
The strain...
When light is viewed from an accelerating frame of reference it appears to bend at a rate of a/c (the acceleration a being at right angles to c). By the Principle of Equivalence the bending of a beam of light in a uniform gravitational field ought to be g/c rad/sec. In principle you could use...
I am studying the finite bending of a rubber-like block, assuming Neo-Hookean response. In the following, ##l_0##,##h##, ##\bar{\theta}## are parameters, while the variables are ##r## and ##\theta##.
The Cauchy stress tensor is
##T= - \pi I + \mu(\frac{l_0^2}{4 \bar{\theta}^2 r^2} e_r \otimes...
This is the analytical working out. I substituted the value of 306mm ( the maximum length of the beam) to find the maximum deflection along the Z-axis. Which came out to be -2.39mm. But according to Ansys the average deflection is 0.3mm and the maximum deflection is 0.8mm.
This is the Ansys Values.
I haven't taken a physics courses in some time and I'm having trouble getting started with this textbook question. I know that there will be relativistic effects present, but I can deal with that. The problem is how I can approach the problem. I initially thought of a geometric way to set up...
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I saw quite a nice Youtube vid about general relativity and how gravity bends spacetime and therefor redirects angular momentum into the center of gravity. I thought the first time I begun to understand the concept but immediatly the questions poped up.
The video basically says...
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Im a bit confused with the example
Can somebody explain and show to me how they got the bending moment calculations for the diagram in the attached. i understand it up to there.
I started course late and can't ask for help.
Thanks
Hello:
I was looking for a widespread convention (akin to Hibbeler's, Beer's, etc) that deals with the sign convention of a vertical bar for bending moments.
For example, without knowing in advance, how do I draw the bending moment at a cut passing through point E in the figure attached?
Beam...
I have to discuss the Bending moment and shear forces in cantilever and encastré beams. Does anybody know of good websites showing that is simple to understand showing. All i can find is how to calculate and bending moments and shear force digrams which don't really understand.
Can...
A cantilever beam 2 meter in length, 5KN act at point (A) of the beam. There is point x it looks like half way along the beam. how do i workout the distance of point X so work out the magnidues of Ra and Rb so i can go onto working out bending motion and shear force?ruff idea i had
1) Ra x 2...
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how can one analyze the telescopic boom of a workshop crane in terms of bending ? Of course the worst case is when the boom is fully extended. Should we treat it as a beam with sudden change of cross-section (or otherwise - with sudden change of flexural stiffness) ? I know that there are...
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I have a question regarding plastic bending of beams (assuming bilinear elastoplastic material - with or without hardening) . In literature one can find calculations of load capacity for those beams. But what else can be calculated in such case ? Stresses ? Deflection ? Where can I find...
There used to be sold a style bicycle handlebar bags that used what I think is a formed spring steel rod that fit over the handlebars and looped under the handlebar stem that supported a handlebar bag. For whatever reason this style does not appear to be available any more. I think it is a...
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I'm trying to solve an exemplary case of a cantilever plate (one long edge fixed, all other edges free) subjected to pressure. I've already calculated this using approximation to beam of unit width and the results are good but I would like to use another method too. In a polish book I've...
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books such as „Roark’s Formulas for Stress and Strain” or Timoshenko’s „Theory of plates and shells” provide formulas for maximum bending stress and deflection for many cases of rectangular plates. However, I can’t find a simple case of a cantilever plate (one edge clamped, all other edges...
I need to figure out how much weight a 96"x48"x6" EPS foam board can hold when laid flat and supported at both ends(96" span). Tensile psi: 92. Compressive psi: 52. I believe these figures are for 10 percent deformation. I would like to support temporary 200lb loads at any point on the span...
So I have a Stylus as shown in above fig. Fixed at Point A, Force (F) is applied perpendicular to the stylus axis. How do we find deflection at the end of the Stylus (Made of Two Different Materials as shown in the figure)? Hand Calculations are much appreciated. Thank you.
Hi. Say you apply a moment on a beam and bend it into an arch. If you take a free body diagram of a section of the beam you would need normal stresses in the radial direction to balance the forces:
I have never seen this brought up before though -- is it correct logic? Also, is this sort of...
I'm using the wikipedia page on Size Effect to get an understanding of it. It identifies Statistical and Energetic size effects and two types within energetic.
I believe I understand statistical, as it seems to essentially say that assuming there's some variation in the material strength, the...
Hello,
I am looking for some help. I have completed the question below. I will show my answers.
My answer:
I believe this to be correct. If it is not would appreciate someone letting me know so i can correct.
Now i am attempting this question:
Could anyone help, or point me in the...
A bending moment about an axis passing through a cross section arises due to an uneven distribution of stress across the cross section, like so:
I have read that any given bending moment is equivalent to a force couple applied about that axis. That is to say that the curly moment arrow on a...
I was reading through a set of notes and found something a little odd. The aim is to solve the beam structure shown below, which is massless and of length ##l##.
By considering the beam as a whole, we obtain ##A_y = P##, ##A_x = N## and by taking moments about A we see ##M_A = Pl##.
However...
Hi all, i need Permissible stress (Shear & Bending) values of various materials that is used for shaft design, as like below.
Is there any software or excel sheet.
kindly let know.
Lets say that a man with a standing height of 185cm bent his knee 30 degrees, how many centimeters will be reduced from his standing height? Assume his femur length is 60cm and his tibia (shin) length is 50cm.
Can anyone give me a hint?
I've tried to use trigonometry but i don't think i fully...
I know the out of plane bending stress equation for a curved I beam but I am trying to figure out where it came from. sigmaR = tFlange * sigmaNormal/(radius of curvature)
I am still new to the theory of relativity (both SR and GR), but I've read few books which gave me an insight about the subject (not a mathematical insight though). There's a question that I really would like to know the answer of: Is there a time delay for the bending of spacetime to occur...
I have a quesrion about forming the eqaution of moment equilibrium.
As shown in the picture at cut 1 there are 2 vertical forces and a bending moment. I expect V=A.
If I apply moment equilibrium about the point where the bending moment is, we get that Ay*x = M(1). But how about if I take moment...