# Beam Definition and 51 Discussions

An I-beam, also known as H-beam (for universal column, UC), w-beam (for "wide flange"), universal beam (UB), rolled steel joist (RSJ), or double-T (especially in Polish, Bulgarian, Spanish, Italian and German), is a beam with an I or H-shaped cross-section. The horizontal elements of the I are flanges, and the vertical element is the "web". I-beams are usually made of structural steel and are used in construction and civil engineering.
The web resists shear forces, while the flanges resist most of the bending moment experienced by the beam. The Euler–Bernoulli beam equation shows that the I-shaped section is a very efficient form for carrying both bending and shear loads in the plane of the web. On the other hand, the cross-section has a reduced capacity in the transverse direction, and is also inefficient in carrying torsion, for which hollow structural sections are often preferred.

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1. ### Leaf spring deflection

Hi, 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...
2. ### B 1-photon emission possible from electron-positron annihilation?

I was reading about electron-positron annihilation. Typically it results in two photons, each with an energy of 511 keV, that go shooting out in opposite directions. But I read that in some instances three photons can result. Electrons have an intrinsic spin of ½, while photons have a spin of 1...

4. ### Elliptical facet cylindrical optical fiber - Mathieu equation

Let's say I have three modes in a fiber that is elliptical cylinder shaped (cylinder with elliptical facet), as in the image below (the source:Optical Engineering, 46(4), 045003 (2007)) so what is the equations that describe these fields..
5. ### Minimium diameter of an electromagnetic beam in terms of wavelength

Is there a limit on the minimum diameter that a collimated electromagnetic beam must have (lasers or masers), in terms of its wavelength, or it is possible to create a beam with its diameter smaller than its wavelength? I'm considering a colimated planar wave directly from the source, and not...
6. ### Deflection of a cantilever beam with applied tension at the free end

Not much to add since the question is fairly simple, but again I'm wondering if applying tension at the free end of a cantilever beam affects the deflection it would have if only its self weight is considered. Intuitively, tension should tend to straighten the beam, and if it does, how to...
7. ### Reinforced concrete beams

When I convert the steel beams to concrete, do I transform the several different beams into a single piece of concrete in order to do the calculations to find the second moment of area of the beam or do I transform each beam seperately into a concrete piece? Intuitively, t seems reasonable to...
8. ### Longitudinal distribution for a neutrino beam

In the center of mass frame of reference i found that ##p^{*}=\frac{[(M^{2}-m_{\nu}^{2}-m_{K}^{2})^{2}-4m_{\nu}^{2}m_{K}^{2})]^{1/2}}{2M}##. I don't know how to find the momentum distribution ##p_{L}(\theta)## considering that i have 2 different mesons with a specific number ratio...
9. ### Irregular free-free beam, non-numerical solutions

What are the simplest, even if not very accurate, non-numerical ways (for example a variation of Euler-Bernoulli) for describing the deflection relative to a given load of a free-free beam with irregular shape (variable second moment of area and/or lumped masses distributed at some points)? In...
10. ### Off-Axis Torque To A Cantilever Beam

I'm interested in understanding how to deal with a torque applied to an angled cantilever beam. The torque is being applied along a horizontal axis at the location of the end of a cylindrical beam. I am interested in how this torque will cause twist along the beam's axis, as well as any...
11. ### Why is a beam supported by two cables more stable than one?

Imagine a steel I-girder lifted by a single wire rope. If the rope is not perfectly centered along the girder length, the girder will rotate about a horizontal latitudinal axis through its centroid. Imagine a girder pair lifted by two wire ropes, with one rope on each side of the girder...
12. ### Find the mass M so that the net torque is zero

Homework Statement Hello, I have a problem I don't want how to approach, it is a little weird. It is a problem of equilibrium (torque) The situation and my approach is in the picture I uploaded. A beam is supported by the blue structure. On the beam it is a person(100N) at a distance of 3m in...
13. ### Can a photon travel slow enough to be seen by the naked eye

Please see my attachment of a recent observation of light traveling through a medium. There is no source, just my observation The packets of light appear to be visible, distinct , moving at different speeds, and display the various colours for each wavelength. Is this normal / possible in a...
14. ### Is Shear Stress Vertical or Horizontal in I-Beam Webs?

My mechanics of materials book states that in order for an element to be in equilibrium it must have equal horizontal and vertical shear stresses. However, it also states "The shear stresses in the web of a wide-flange beam act only in the vertical direction and are larger than the stresses in...
15. ### Finding a maximum force in a beam type system before failure

Homework Statement See attached photo Homework Equations Stress = F/A Area = pi d^3 / 4 Sum F h = 0, Sum F v = 0, Sum M = 0 The Attempt at a Solution Hey everyone, after reading the question a number of times and not knowing for certain where to start, I figured because the stress and area...
16. ### A How could we produce a secondary beam of long neutral kaon

how could we produce a secondary beam consisted of long neutral koans using PS or SPS ? I mean is there any example of such an experiment? what are the conditions for conducting this such as the type of the primary beam, the type of the target and the momentum of the beam? Im interested to...
17. ### Maximum moment question

Hey guys, I've been reading my strength of materials textbook and its pretty much like a reviewer that contain several problems and short descriptions of their concepts. There's this formula that computes the maximum moment for two moving loads and its: [PL-(Psmall)(d)]^2/4PL where P= Psmall...
18. ### Help with a BMD and deflection of beam problem

Homework Statement I am given this beam: imgur link: http://i.imgur.com/tw6EEJz.jpg and asked to express the slope at A and the max deflection in terms of a, E, I, and Mo. I am being told that my answer has the wrong multiplier...so I assume that my overall approach is ok (??) but I've...
19. ### Transfer of forces from a pulley to a beam

Homework Statement I am trying to understand how forces transfer from a wheel / pulley onto a beam, and then calculating the resulting moment. The image describe the problem. The rope is in tension with force "S", the wheel/pulley can rotate freely without any friction. Homework Equations...
20. ### A Anisotropic pinch force in high energy electron beam

Here I am only considering 4 adjacent electrons in electron beam, especially the 2 electrons that are moving in tandem with velocity v. Moving charge will generate circular magnetic current. you can imagine magnetic flux as current, just like electric current. So, the question is same to find...
21. ### Deriving Strain in Cantilever Beam with Known Deflection

I am trying to derive the strain at the base of a cantilever beam with a known deflection. I know the bending stress is equal to Mc/I, so the strain is Mc/IE, where c is the distance from the neutral axis. For a point load ,P, the strain would then be PL/IE. Since the deflection is known I...
22. ### Strain of a Cantilever beam

Hi, Well i have a system with a excited (in y axis) cantilever beam. I struggling to obtain a expression that gives the strain based on the dislocation y. I know that the displacement of the beam is given by: Ya=PL^3/(3EI) but how i make a correlation between this and the strain of the...
23. ### Finding weight of a beam using torque & equilibrium?

Homework Statement A uniform beam at equilibrium is suspended by a cord at X which is 2m from one end of the beam and and 3m from the other end. There is a mass of 28N attached to the 2m end and a mass of 10N on the 3m end. Determine the weight force of the beam Homework Equations...
24. ### Deflection of beam

Homework Statement I am trying to find the maximum deflection in a brass beam, however after taking a physical reading the theoretical answer I get is quite off and I am wondering what I am doing wrong. Homework Equations They tell us the max deflection is( Load*Length^3)/(48*E*Second Moment...
25. ### Reaction force in a beam

Homework Statement Calculate the reaction force at A? Homework Equations ΣMb = 0 The Attempt at a Solution As there is a pin joint at B it is possible to consider the bar only from A-B. From here I applied ΣMb = 0 120 + 20*2 + Ay*4 = 0 This gives Ay = -40kn Also since there are no forces in...
26. ### 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...
27. ### How do I represent load distribution of over hanging object

I am trying to make a FBD for equipment which is half out of the beam, I realise I can represent it with a single line of force. But how if I want to go for distribute load? which one is the correct one. (purposely not drawing reaction force on floor.)...
28. ### Beam Deflection equation question

regarding this equation, δ=(PL^3 )/(48EI) For the calculation of maximum deflection, if my structure is not longer a full form beam (meaning the structure has 6 holes drilled to it), can this formula still be used?is...
29. ### Beam Bending Question

Bonjouro! Firstly, as this is my first post here, I would like to say thank you to everyone who is a part of the site and Hello! I've used this forum a number of times, but this is the first time I've posted here as this user! If the flexural stiffness of a beam is 25 MNm^2, and the beam is...
30. ### Plate Buckling Deflection Function for Rayleigh Ritz Method

G'Day Everybody, I am computing buckling of a rectangular(edges: a*b) specially orthotropic composite plate. The boundary conditions are clamped-clamped at the opposing loaded edges and the other two edges are free (also known as CFCF). After having the boundary conditions and the governing...
31. ### Force/Stress Along a Beam

Homework Statement Two beams of different cross sectional areas are fused together to create a single beam, as shown in the figure above. The following relationships apply: A1 = 2A2, L2 = 2L1, E1 = 3E2. A tensile force F is applied at the ends of the bar, as shown. What is the ratio of the...
32. ### Derive Euler–Bernoulli equation from Navier-Cauchy equations

Hello Is it possible to derive the Euler–Bernoulli equation: \frac{d^2}{dx^2} \left(EI \frac{d^2w}{dx^2} \right) = q from Navier-Cauchy equations: \left( \lambda + \mu \right)\nabla\left(\nabla \cdot \textbf{u} \right) + \mu \nabla^2\textbf{u} + \textbf{F} = 0 I don't really know where to...
33. ### Deflection in a Cantilever beam

Hello, i was looking for ways i can reduce the deflection in the cantilever beam whose one end is fixed and load is applied at the free end. Few i thought of was, 1- Reducing the length of the beam 2- Increasing the modulus of elasticity of the beam 3- ?? 4- ...
34. ### Microparticle Transport via Directed Particle Gun

Greetings PFers, Would it be possible to move microscopic particles of a wide range of composition (conductivity, density, etc...) using a directed beam technology? The idea is to have a fast 3D printing technology (practically no moving parts) that is capable of depositing of a wide array of...
35. ### Nonlinear Mass Spring Damper with Euler Bernoulli Beam

I'm trying to find a solution to a system in which a clamped free Euler-Bernoulli Beam system rests on top of a mass-spring-damper system. The MSD system has nonlinearities in both the spring and the damper and is of the form: I have extended the nonlinear restoring force to its 3rd term and...
36. ### Beam Analysis for Indeterminate Beam with Overhang

1. The problem, I have a beam 9000 mm in length. assuming a x-coordinate system: supports are at the x= 1500, x= 4500, and x= 7500 positions. there's a uniformly distributed load (let's call it w) through the length of the beam (from 0 to 9000mm) Solve for the MAXIMUM moment. This would be much...
37. ### Bending stress

Hey everyone, I was just wondering if someone could explain to me what Bending stress is? Supposed you have a cantilever beam with a point load at the free end, I know that the bending stress will decrease as you move away from the fixed end? but why? and how can you back that up? Also, as...
38. ### Fourier series, is this valid?

Hi, I have a Fourier problem that i do not know if it is valid to do the calculations like this. The Fourier transform looks like this ## \hat{v}(x,\omega) = \frac{\hat{F}(\omega)}{4(EI)^{\frac{1}{4}}i \omega^{\frac{3}{2}}(\rho A)^{\frac{3}{4}}}\left[ e^{-i\left[\omega^2 \frac{\rho A}{EI}...
39. ### Fourier Problem, Wave Problem

1. A transversely directed transient force F(t) acts at the free end of a semi-infinite beam. a) Show how displacement, velocity, acceleration and strain at an arbitrary position along the beam can be determined. b) Calculate (MATLAB) the transversal acceleration (or an other quantity) at an...
40. ### Tapered Cantilever beam

Hey all, So I have this beam problem and I honestly am lost with it! The beam is I-section cantilever, tapers in depth along its length (See picture attached) with a point load at the free end. Im trying to figure out the deflection formula and how to derive it! Also, when calculating its...
41. ### Bending of a Free Beam

Consider a beam with an upwards concentrated force applied to its center. This is equilibrated by a distributed downwards force. There are no displacement boundary conditions. I've tried approaching this with simple beam theory, but I can't get a complete answer (shear, moment, slope...
42. ### Beam deflection equation

I have A beam of 1.2 m long, supports at 0m and 0.8 m. forces of 10 N at 0.4 m and 5N at 1.2 m I need to find the deflection equation for this situation. Can someone have a look and see if they can come up with the equation. As I have tried but my results do not match what I am expecting
43. ### Creating a spring using only beams

Attached is my ANSYS model of a spring made using cantilever beams. In playing around with with different dimensions, I noticed that the longer I made the connecting section (dirty green section) the less of a total deflection there was. Could someone explain to me why this is? The overall goal...
44. ### Bucklig: deflection at Euler load

Hello I was trying to calculate the horizontal deflection of the free end of vertical clamped beam. The beam would be loaded at the free end with a horizontal force H and a vertical force P. My idea was to calculate an initial deflection due to the force H. Then calculate the additional...
45. ### Vibration of a cantilever beam

Hi there! Im trying to do an analysis in Abaqus of a cantilever pipe, with a tip mass at the free end, that is decelerating to a stop at 10 m/s2 from 10m/s, causing it to vibrate. To validate my results im doing some handcalcs. I have done a static analysis and calculated the maximum deflection...
46. ### Structural frame analysis

Homework Statement Hello. I've created a small program to find shear and bending diagrams of the members of a frame. I was able to get the reactions at the support but don't know how to continue from now. This is an example of a frame all columns are 3m in height and the beams 8m. All the beams...
47. ### Inclined Beam with UDL

Homework Statement Hello all, I am trying to find the deflection of a hydraulic cylinder at point A (refer the attached). There are two hydraulic cylinders, with certain distance apart. On top of it is a beam that is inclined to the horizontal by 12 degrees. The piston is operated by two...
48. ### Straight light beam in opaque water

Hello! As this is my first post - I'm Mike from Poland, currently studying product design on Academy of Fine Arts in Warsaw. I'm working on a sculpture - light installation. I want to achieve an effect of a regular beam of white light - light cylinder in slightly opaque water. Sort of similar...
49. ### [Antenna Beam Forming] Antenna Pattern & Element Pattern

Hey guys, currently I am working on my diploma thesis in the field of beam design for mobile communication. I created a linear array with N elements and computed the corresponding Array Factor with the help of the chebyshev distribution. I assume my Element Factor to have its maximum at 90°...
50. ### Cubic phase modulation of a gaussian beam

Hi all, I'm reading a paper on light sheet microscopy, i won't go into detail here but they are generating the light sheet by use of an Airy beam. They are using a term i don't understand when describing how the airy beam is generated. Quote "An Airy beam can be generated through the Fourier...