Questions tagged [beam]

Questions about the theory and applications of structural elements designed to resist bending.

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18
votes
7answers
5k views

Is it structurally sound to cut an I beam to a T on one end?

I'd like to confirm whether the replaced beam in the attached picture is structurally sound given the end was cut to a T instead of an I. I had a qualified structural engineer approve the work but I'm ...
13
votes
4answers
1k views

Easy nonlinear model for large deformation of a beam

I have a beam subject to twisting and/or bending forces as well as linear compression force along its main axis. It is modelled as an isotropic beam, but if anisotropic is not too far off then that's ...
12
votes
1answer
6k views

At what point does an I-beam becomes a H-beam?

According to BS5950, a beam section can be classified as plastic, semi-compact, compact or slender. For the same section area, a H-beam can take axial compression (without buckling) better than an I-...
12
votes
4answers
7k views

How do I calculate the forces on a desk and its legs?

I have a design for a desk, and I'd like to not just guess at how strong it'll be, but I can't find an explanation on how to figure out all the forces involved that doesn't assume I already know a lot ...
11
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2answers
4k views

Buckling: Do buckling mode shapes of n > 1 occur in reality?

In the buckling of columns we know that: $$P = \dfrac{n^2\pi^2EI}{L^2}$$ The smallest value of P occurs when $n=1$ which gives a simple buckling shape (one wave): $$P_{cr} = \dfrac{\pi^2EI}{L^2}$$ ...
10
votes
3answers
3k views

Strength of a welded steel gate with vertical bars vs. crossed diagonal bars

Looking for some hints on how to create a rough estimate for the following problem. Given two steel gates with the same dimensions, same material - e.g. everything is the same. The only difference ...
10
votes
3answers
6k views

Why is it unwise to choose cylindrical horizontal beam

I heard that it is unwise to choose cylindrical horizontal beam. My question is why?
10
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2answers
33k views

How to deal with a point force acting right on the hinge of a beam?

I have been attempting to solve a question where there is a point force acting on the hinge of a beam. Here is the problem: I am not sure how to deal with the 2 kN point force at $C$ ($C$ and $E$ are ...
10
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3answers
4k views

How do you select the correct area to consiser for first moment of area calculations?

I have just begun studying mechanics of materials and I am struggling to understand intuitively how to select the area in first moment of area calculations. I was hoping someone has a relatively easy ...
9
votes
1answer
3k views

Derivation of the weak form for the euler-bernoulli beam equations

I am master student and doing an assignment of Finite element method. In the instruction I could not understand the derivation of the weak form, which should not be difficult. I'm sorry for posting ...
8
votes
2answers
4k views

Unbraced Length for Lateral Torsional Buckling vs. Yield Strength

The AISC 360-10 Specification for Structural Steel Buildings gives provisions for calculating the maximum unbraced length of a compression flange that separates yielding moment from lateral torsional ...
8
votes
1answer
2k views

Large deflection of a cantilever beam with distributed normal load

I have a strip of stainless steel encastree'd at one end to which is applied a constant pressure on one side, and I need to know what the deflection equation y = f(x) is at equilibrium. If the ...
8
votes
2answers
910 views

Design of transverse reinforcement in a wide beam

Besides satisfying nominal bar provision in the code, is there any special requirement in the provision of transverse reinforcement to ensure that the longitudinal reinforcement is fully effective in ...
8
votes
3answers
820 views

Tolerance for Beam With Cope End

I need to have some beams fabricated with copes on the ends. They will be set on top of existing steel trusses, and used to replace undersized purlins to shore up existing rafters (hence the need ...
7
votes
2answers
432 views

What does it mean when actual member reaction is 100% of allowed?

I received construction documents for an extensive residential remodel and looking at the engineering there's a glulam drop beam with a calculated member reaction that is 100% of allowed (3965 lbs @ 5 ...
7
votes
1answer
394 views

Energy of a 3D Timoshenko beam

I am interested in the kinetic energy T and the potential energy U of a three dimensional Timoshenko beam. For a 2D Timoshenko beam the energies read: $$ T = \dfrac{1}{2} \int\limits_o^l \left( \rho ...
6
votes
4answers
9k views

How do you calculate Mcr (critical buckling moment)

When designing a steel beam, the resistance to buckling is related to Mcr; the elastic critical moment for lateral-torsional buckling. However the Eurocodes give no advice about how to calculate this ...
6
votes
1answer
3k views

Strength of a Vertical Round Aluminum Tube with load cantilevered off it?

Can a vertical round tube safely support a cantilevered arm mounted near the top of the tube? ROUND VERTICAL TUBE: 6061 Aluminum 2 inch Outside diameter 0.25 inch wall thickness 3 feet height ...
5
votes
3answers
3k views

Does the length of a beam change upon deflection?

I have made a Python program in which I have computed the deflection of a beam. I am plotting the deflected beam and am now asked to show the length of the beam. If the beam is not deflected, it is ...
5
votes
2answers
171 views

Effects of constructed tubular/annular beam upon moment of inertia

I would like to construct a hollow beam using either 2"x4" or 2"x6" structural lumber.1 My thought is to take 4 boards and butt them against each other in order to form a square beam2 with a hollow ...
5
votes
1answer
3k views

What is the mathematical derivation for shear center of a beam?

For me, it's a bit hard to imagine where shear center can be, and what purpose it serves. The definition I found online is very vague: Shear center is defined as the point on the beam section where ...
5
votes
1answer
171 views

Why is this box girder made of lattice on one side only?

Here's a zoomed piece of this image from Wikipedia That's a close-up of a tower holding a railroad bridge. A and B are two of the four columns in the tower's corners. I assume that they are placed ...
5
votes
1answer
87 views

"Heavy-duty" or not, can my drawer slides really support this weight?

Okay, so recently I got a Dewalt 735 Thickness Planer. It's great at what it does. (It even LOOKS like it's ready to consume the tender flesh of lumber, like some twisted Victorian lumberjack... ...
5
votes
2answers
152 views

Longitudinal impact of steel rod on a steel plate to verify the contact duration

So I'm doing an experiment to verify the contact duration when a steel rod (Material: Mild Steel) is allowed to free fall longitudinally on a steel plate. The arrangement is real simple: The rod is ...
5
votes
1answer
84 views

Can the thickness of a guard post be derived purely from energy principles?

Consider an ordinary staircase with a banister rail supported by a wall at one end and a steel post of constant profile at the other end. The base of the post is embedded rigidly in the fabric of ...
5
votes
2answers
213 views

How to analyze a bent beam: Stress concentration?

I am analyzing a beam, that has a bend in it. Intuitively and inspecting FEA results using a linear solver, there is a stress concentration at the bend of this I-beam. The part was not a straight I-...
4
votes
4answers
4k views

How does stiffness/rigidity affect the bending moment of a beam

My question may sound silly as it’s mainly good sense but I may be mixing things up. Let’s consider a flexible cantilever beam of a given length and material is fixed at one end and free at the other ...
4
votes
3answers
5k views

Why does a continuous beam have less deflection than a pair of simply supported beams?

Inspired by this question, and also this answer to a separate question. I have two beam models, one with two independent spans (a full hinge), another is a continuous beam over both spans (only ...
4
votes
2answers
2k views

Given the tensile strength of a rod, how do you calculate the max weight that can be hung from it?

Given a 3.25" long, 0.125" diameter rubber rod with tensile strength 1200 psi supported on both ends, how much weight can you hung from the middle of it without breaking it? (This is not homework I am ...
4
votes
1answer
2k views

Derivation of beam slope for a cantilever beam

I am trying to derive the maximum beam slope formula $\theta = \dfrac{wL^3}{24EI}$ for this cantilever beam: What method can I use for this derivation? So far I can only find simply supported beams ...
4
votes
2answers
79 views

Beam buckling criterion?

If I have an I beam which I subject to some bending load, how can I calculate when the thinner middle part of the I beam will buckle? I though I could use Euler's critical load formula here, but it's ...
4
votes
2answers
953 views

Degrees of freedom of an internal hinge in plane beam?

What are the degrees of freedom of an internal hinge in a plane beam? I understand that the bending moment=0, does this mean there is no slope either? Or does it have both degrees of freedom of ...
4
votes
3answers
10k views

Are the points of inflection and contraflexure the same?

In theory of bending of beams, often these terms are used. There are no clear definition present. Most of them contradicting. Which of the property(bending moment and shear force) is zero in which ...
4
votes
1answer
320 views

Why are steel I-beams mostly symmetrical?

From what I understand most types of steel are strong both in tension and compression, yet they are still usually significantly stronger in tension. Suppose a common I-beam supported on both ends and ...
4
votes
2answers
4k views

Round beam deflection under its own weight

I'm trying to calculate how much simply-supported round beams of several materials and diameters deflect under their own weight plus an additional weight in the middle. I know the material densities ...
4
votes
3answers
2k views

How is shelf deflection determined?

Question: How is shelf deflection determined? More specifically, how is the deflection determined when one or more edges of the plate have reinforcing edging applied to them? I have been able to find ...
4
votes
2answers
7k views

Multiple Varying cross section beam deflection

How do we calculate the deflection of a cantilever with two or three cross-sections, and different forces acting at the end of each section?
4
votes
1answer
122 views

Torsion and Bending stress calculated from deflection

I need help to check a calculation I did. I want to know if it is possible to use this method or if I am using an assumption which is wrong. Let me explain the problem, a beam with length $l$ is ...
4
votes
3answers
142 views

Natural frequencies of an orthotropic bending beam with circular cross-section

I am trying to find an expression for the natural frequencies of an orthotropic bending beam with a circular cross-section. I have tried searching for some literature on this, but have so far been ...
4
votes
1answer
136 views

Skewing of joints using virtual work

Given ist the following framework: $$E=210 \frac{\text{kN}}{\text{mm}^2}$$ $$ EA \to \infty $$ $$ I_1 = 80000\text{cm}^4 $$ $$ \frac{I_1}{I_2} = \frac{3}{4} $$ $$ I_3=I_1 $$ Using the principle of ...
4
votes
3answers
660 views

Are linear beam element solutions ever exact and when are they used in practice?

In qualifying the results of a Finite Element (FE) beam model, I'm realizing that I dont understand FE beam elements as well as I should. Is there a procedure to determine what order beam element is ...
4
votes
2answers
154 views

Undesired vibration of a beam under foot traffic

The other day I was in the waiting room of a doctor's office in a new building as part of UCLA medical complex. A new construction as part of multi million dollar extension of existing medical complex ...
4
votes
1answer
2k views

Deriving the deflection force equation for a beam that is fixed on both ends

I want to calculate the force-displacement equation for a beam that is fixed at both ends. I think I should use the superposition principle but I am not very sure how to get started. I know that for,...
4
votes
1answer
172 views

Is the order of operations in jacking a cable relevant?

If you have a prestressed concrete beam or slab and are jacking a cable from both ends, does the order of operations alter the result? For a symmetric curve, the tension diagram along the cable's ...
4
votes
1answer
117 views

Deformation of two perpendicular beams with parabolic properties

I want to calculate the deformation of the following structure: I have numbered the vertical beam 1 and the horzontal beam 2. The hight of beam 2 is given by: $h(x)=h\sqrt{1-x/L_2}$ So I thought I ...
3
votes
3answers
7k views

Why do we assume the moment is zero when analyzing a simply supported beam?

When calculating the reactions of a simply supported beam under any type of loading we assume that the moment about the reaction points is zero. What if our assumption is wrong and in actual practice ...
3
votes
3answers
116 views

Why does concentrated shear force on a beam influence the whole beam?

This might be a silly question but can someone explain how this shear force on the right side of the beam causes Qy throught the whole beam? I understand it mathematically but not conceptually so I ...
3
votes
2answers
11k views

Determining stiffness of a beam w/varying moment of inertia

I need to calculate $K$ or equivalent stiffness of a beam that has a varying $I$ across its length. $I$ has been given to me as a function of $x$, or length. I have been unable to find a proper ...
3
votes
3answers
4k views

Is it possible to convert uniform loads to point loads?

I want to perform a structural analysis on a portal frame using a finite element solver to get a displacements and reactions for a load. The software library only accepts loads applied to node, not to ...
3
votes
2answers
1k views

Why is there a moment at the cross section end when you cut a body?

I just started mechanics of materials, and it seems that my knowledge from statics has gotten rusty over the summer. But there was a new concept introduced in the first example problem today. There ...

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