Questions tagged [structural-beam]

A structural element whose length greatly exceeds both its width and height, which are of the same order of magnitude.

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Doubt in derivation of bending of beam, It's about derivatives and intergration

Radius of curvature of the beam in above picture is given as: $$ \frac{1}{R} = \frac{d^2 y}{dx^2}$$ Please help me two points used as steps of a derivation in my book: How was the radius of ...
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Why two wires are used in railway overhead equipment? [closed]

While watching the train video's I came across this overhead wires. After searching on internet I found that both catenary and contact wires carry same voltage and connected by vertical wires called ...
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Deformation of gradually applied load vs impact loads?

When a load P is applied gradually on an object, the work done on it is the average of the initial and final loads, which is generally P/2 multiplied by the deflection Δ1. In the case of impact load, ...
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Inconsistent units in modal analysis of vibrating beam

(read the last sentence for the actual question). Consider an elastically suspended solid body from a massless cantilever beam The equations of motion of such a system are $$\begin{bmatrix}m\\ & ...
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Do inertia affect stiffness matrix of beam?

Refering to a pdf I uploaded at here. Why does these stiffness matrix displacement do not need to consider the inertia (determines the shape of cross-sectional area of each element) ? I have always ...
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An intuitive reason for the fourth derivative in the beam equation?

The appearance of the second derivative (or Laplacian in higher dimensions) in the diffusion equation ($u_t=u_{xx}$) and the wave equation ($u_{tt}=u_{xx}$) seems intuitive to me. The quantity simply ...
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The state of a Stress element isolated from a beam

Consider a beam subjected to an arbitrary loading, where the loads are only present in the plane of bending. The x-y plane is the plane of bending. If I take a stress element in the beam, there will ...
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Free response of plucked string

Based upon points $x=l/4$ and $x=l/2$, how would one determine the relative error between the free response at $t=0$ and the exact initial deflection as a function of mode numbers contributing to the ...
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Twisting Solid Steel Bar - Annealed, Hardened or Doesn't mater? [closed]

Workshop project underway... Been decades since I was in a physics class. Building something out of steel - options are mild steel 1018 and alloy steel 4140 that can be hardened by heat treatment. ...
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How a fixed support which allows lateral contraction and expansion will look like?

I stumbled upon an exercise problem wherein it was asked to calculate the change in lateral dimensions of a bar fixed between two immovable supports, when temperature of the bar is increased by $\...
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Stress in a bar subjected to unequal forces [duplicate]

A bar is subjected to force P at one end and 3P at other end, what is the stress developed in the bar and will it vary along the length of bar ? Is there any stress due to inertia force? According to ...
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Stiffness of a Cantilever Beam

I was wondering that for a Cantilever beam subjected to point load at extreme end. Does the stiffness goes on changing as the deflection of free end changes? Logically it should provide more ...
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Would bolting four 3" square tubes to an existing 3" square tube (one per side) increase rigidity? [closed]

I had a pier fabricated for my telescope consisting of a 1/4" steel plate, 10" diameter, bolted to a concrete pad. A 3" by 34" square steel tube is welded to the base plate and ...
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Can I approximate an electron beam in the air to a Gaussian beam?

We have used an electron beam (with energy of 6 MeV, used for treatment of cancer patients) and calculated the received dosage. The experiment was set up with a stationary sensor at length ...
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How does the load on the tip a cantilever affect how long it continues vibrating after release?

I'm considering a situation in which a load is applied to the tip of a cantilever. After the release of the load, the cantilever oscillates, but due to an energy loss to the environment (which I think ...
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Derivation of dynamic nonlinear equation of motion of cantilever beam

Is it possible to derive the EOM of an inextensible cantilever beam without using any kind of variational principle I mean is it possible to derive it from Newton's law only? Note: of course This ...
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Difference between bending equation of cantilever beam and dynamic equation of motion

What is the difference between Bending Equation of cantilever beam and dynamic equation of cantilever beam? Is it possible to derive one from the other?
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Angular damping on a cable segment caused by internal friction

I'm using a physics engine to simulate a cable made of cylinder-shaped segments connected by ball socket constraints. My understanding is there will be some angular damping on the segments cause the ...
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What is the mathematical description of a point torque (or point couple) singularity?

Suppose that a concentrated (point) force is exerted at the origin of a 3D dimensional space along the direction $\boldsymbol{e}$. Mathematically, this could be prescribed in terms of a delta Dirac ...
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Will a platform only supported by a column in the center fall? (Excluding weather)

My friend told me that without wind, a building with a platform that only has a column supporting it would be balanced and not fall, given that there is no wind. I said that the platform would fall ...
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Adding tension to a model of a Timoshenko beam?

I am interested in modeling a Timoshenko beam. However, I would also like to add tension to the beam so that it can vibrate like a string as well as a beam. The Timoshenko beam is described at that ...
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How is this basic equation of a Timoshenko beam derived?

I am trying to learn how to model a Timoshenko beam which is described here: https://en.wikipedia.org/wiki/Timoshenko%E2%80%93Ehrenfest_beam_theory There are a few things I can't understand but the ...
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Why is shear force half the total force?

When applying a perpendicular force to a beam which is fixed on either side then the shear force is given by $V=\frac12 F$. My intuition says that this is because the force $F$ is distributed over two ...
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Catenary shape of transmission lines

When flexible metal transmission lines are hung between two poles, the shape they assume to minimize the action of gravitational and tensile forces is a called a catenary. While assuming that shape, ...
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Swords and wing flutter

In order to retain structural integrity it is understandable that a sword has to be flexible enough to be able to absorb impact without shattering and rigid enough to not be bent due to it. Is this ...
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Simple cantilever beam deflection - what is the simplest way to add a damper?

I am looking at a simple cantilever beam deflection: I understand the general expression for deflection/force would be: $y_s = \frac{Fx_s^3}{3EI}$ $F_p = \frac{3y_sEI}{x_s^3}$ If you were going to ...
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Why buckling is described by the maths of the harmonic oscillator?

Is this a coincidence or there is a more deep connection between the notion of the harmonic oscillator and the notion of buckling?
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How do I account for damping on structural vibrations?

I want to know what terms to add to the differential equation for structural vibrations to account for structural damping. Not external damping, but internal damping. I consider the transfer of energy ...
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Tower of building blocks

Why does a tower of building blocks (cubes) fall? Theoretically, as long as the center-of-mass is above the blocks' bottom faces, and as long as one does not shake the tower too much, it should not ...
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Shear stresses in a rectangular beam

To find the shear stress at point A in the beam above using the equation τ=VQ/(It), how do you decide which value of thickness to use? Is it correct to use a value of 100 mm because the cut segment at ...
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Why does the LASER beam quality factor (M^2) use squared value?

Why does the LASER beam quality factor (M^2) use squared value? Why not using just M? i.e., Why define beam quality factor as $M^2 = \frac{BPP_{Real}}{BPP_{fundamental}}$ not $M = \frac{BPP_{Real}}{...
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Intuitive approach to cantilever deflection based on beam length

A high schooler like me asked a question on here regarding the equations used for cantilever deflection, inquiring about derivations. It turns out the derivation is learnt in the first or second year ...
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Using preload to resist bending moment on an unfixed cantilever beam

I have a cantilever beam that is resting against a wall (not fixed) and will not slide (strictly looking at bending moments). The beam of length = $0.3 \;\text{m}$ is under a distributed load of $4000 ...
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How does stress "propagate" in beams?

I'm studying structural mechanics and I have been stuck on a thought. I drew a very simple cantilever beam situation. If I make a fictional cut like in my fig.1, I will be in the situation of the ...
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Do I have to compute the second moment along principal axes to calculate the maximum deflection of a cantilever beam with irregular cross-section?

Do I have to compute the area moment of inertia along the principal axis of the cross-section, in order to find the maximum beam deflection of a cantilever beam with a random polygonal cross-section? ...
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Timoshenko Beam with sliding boundary conditions at angle

I would like to calculate the effective stiffness of a structure which can be represented as follows: (Image source: Link to paper with image.) The yellow part is flexible and the blue is a rigid-...
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Confusion between statically determinate and indeterminate beams

Why is it that statically determinate beams can take some degree of misfits without any generation of strains or stress, but not statically indeterminate beams?
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Differential Equation - Why do beams break?

I've never studied physics before and I'm a Maths major. But I do have a physics-related differential equation question which I need help on. Given the beam deflection equation: $$F(x) = EI \frac{d^...
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Best location for supports of a horizontal beam?

What are the best locations for placement of $y$ supports for a beam of length $x$? This seems like a very basic physics question, but I have been unable to find the answer. Perhaps I am not sure ...
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Euler beam equation sign confusion

Euler beam equation is defined as follows: $$M=-EI{\frac {d^{2}w}{dx^{2}}}$$ There is a negative sign, so if the second derivative of the deflection is negative, the moment is positive. When the ...
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Deflection of L bracket [closed]

I want to calculate the deflection for an L bracket like https://imgur.com/a/0PabX0T to determine how thick I will need to make the steel for a workshop shelf. I have done the calculation using the ...
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Cantilever Beam Deflection with load in middle of beam

How can I calculate the deflection of a Cantilever beam if there is a load at different points on the beam? My current scenario is the following → I have a ruler that I have modelled to be cantilever ...
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Cantilever beam with a mass at different positions and resonance frequency [duplicate]

I have a Cantilever beam attached to vibration generator at the bottom. I have a piece of blu tac of some mass and I move it down the ruler. Whilst moving it down I notice the resonance frequency of ...
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1 vote
1 answer
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Calculate impact force. when A beam starts to fall down with one end hinged and hits an object [closed]

A beam of 10 Kg and length 12 meter starts to fall from initial vertical position with one end hinged. When Beam's center of mass is dropped 5 meter from earlier position, Beam hits an object with ...
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Resonance Frequency and Centre of Gravity

Is there a relationship between these 2 As of now I am moving a piece blutac up and down a ruler to change my COG. I have connected the base of my ruler to a vibration generator and am measuring the ...
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Dependence of resonant frequency on the length of a ruler

Why does the resonance frequency of a ruler increase when the length is lower? I have a relationship from experimenting but I want to know why. I have a vibration generator hooked up to the bottom ...
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2 answers
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A question about the vertical part of the beam

I am solving beam type of problems finding reactions, moments...my question is how do I represent the F2 force that is acting on the vertical part of the beam (on the stick). Usually there is only a ...
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Finding distance of forces for maximum bending moment

I'm having a hard time looking for the distance ($x$) on which the forces must be located for a maximum bending moment. The reaction forces in $A$ and $B$ are dependant of the value of $x$, and so ...
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Can someone explain why there is a discontinuity in beam's Shear Force Diagram with a third support? [closed]

Here is an example: https://beamguru.com/online/beam-calculator/?save=02461c5130daee73a8c73a51060e2adc The reaction forces are $R_a$ and $R_b$. But when it comes to the Shear Force diagram after the ...
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Why is the shear force of simple beam "half-positive" and "half-negative"?

Why is the shear force of simple beam "half-positive" and "half-negative"? As given here: Perhaps it's because the forces have to sum somehow? But does it make empirical sense that the force ...
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