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52 views

Modification of Beam Equation for Thin Sheet

I am trying to determine the modulus of elasticity (Young's Modulus) for a rigid paper sheet. The issue I am having is that my results for the Young's Modulus change depending on what orientation (...
0
votes
2answers
58 views

Pin joint system displacement question

A pinned system comprising bars of the same material and cross-sectional area is subjected to a vertical load P. I am required to form a relationship between FAB and P. The first part of the ...
2
votes
1answer
78 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. When I was learning about ...
1
vote
1answer
84 views

Calculating area moment of inertia for a beam with underslung plate?

In a number of designs, a beam will have an underslung welded plate attached, as shown below: In this sketch, a symmetrical standard steel beam/column of dimensions H1 x B1, with web and flange ...
0
votes
1answer
71 views

Along which direction is the area moment of inertia taken in bending moment equation?

Is it in the same direction of the applied load or in the co-planar perpendicular direction to the load applied?
0
votes
2answers
166 views

Statically indeterminate fixed-pinned beam problem

F=32KN; Mf1=60KN-m; Mf2=-58KN-m; g=30KN/m I need to solve this using Force method. Find the reaction at the pinned end.
1
vote
2answers
723 views

Stiffness of a cantilever beam

I am working on calculating the stiffness of a cantilever beam by applying a distributed load. I wanted to ask if the distribution of the load on the beam effects its stiffness. For eg., if I apply a ...
2
votes
0answers
63 views

What is the optimal shape of a beam subject to three point bending?

Assume we have a beam with density $\rho$ that is subject to three-point bending according to the image above. The beam cross section is rectangular with the variable height $H(x)$ and constant width $...
1
vote
0answers
282 views

Derivation of Bimetallic Strip Stress in Roark's Formulas

I am trying to understand some analytic expressions given in the handbook Roark's Formulas for Stress and Strain for bimetallic strip stresses. Namely, Roark's Formulas give the formulas $$\text{...
3
votes
4answers
887 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 ...
1
vote
1answer
37 views

What's the second moment of a T beam with a heel? [closed]

The second moment of area of a rectangle is $I_{yy} = \dfrac{bh^2}{12}$ b : base h : height What is the second moment of area of a T beam like this one?
1
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0answers
55 views

How much (uniformly distributed) weight can this L beam support without bending? [closed]

As you can see in the picture, the L beam is 1in x 1/2in x 1/8in thick x 72in long and is made of ASTM A36 steel. It's bolted onto a vertical upright on both ends. What is the maximum uniformly ...
3
votes
1answer
107 views

Should one use multiple elements through the thickness with multiple materials?

To get realistic results from a FEM calculation, it is common (or so I've been taught by someone who may not be up to date) to use at least four or five elements through the thickness of a beam or ...
1
vote
2answers
516 views

Deflection of a cantilever beam composed of separate (not bonded) planks

In the case of a simple cantilever beam having a uniform shape and being loaded at its end - the calculation of the deflection at any point along the beam is well known. What happens if we split it ...
2
votes
1answer
222 views

Timoshenko Beam Theory for Quasistatic Cantilever Beam: Shear Term

I'm trying to determine the effect of shearing force on the deflection of a quasistatic cantilever beam. In his book, Theory of Elasticity, Timoshenko added the following term to the deflection: $$\...
2
votes
2answers
54 views

How to find a beam for my (simple) application

I have a spanof 9m that I bridge with a (as yet unspecified) beam. From this beam hangs a load (a pipeline), right in the middle, of 4.295 kN. The beam is simply supported. I want to use an IPE steel ...
0
votes
1answer
81 views

How does the superposition principle relate to Bernoulli-Euler and Timoshenko beam theory? [closed]

I have a shaft with a bearing in each end, and a large eccentric mass covering the entire "free length" of the shaft. The attachment of the eccentric mass is done using heat shrinking. Without ...
4
votes
3answers
87 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 ...
-1
votes
2answers
155 views

Engineering mechanics(statics) [closed]

I don’t get how to get the answer to part e. Should we assume reactions at A and B in all three figures are same? If so, why?
1
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0answers
1k views

Equivalent spring of beam supported by springs

My professor gave us yesterday a problem to calculate the equivalent spring of the system shown in the attached figure. The problem: a cantilever beam supported by two springs $k_1$ and $k_2$ located ...
1
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0answers
759 views

Simply Supported beam with multiple point loads and distributed load [closed]

How can I solve this problem using FEM (longhand calculation)? I want to find deflections at each load point. This is not a homework problem. This is related to a project that I and my brother is ...
4
votes
3answers
4k 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 ...
0
votes
1answer
278 views

How to deal with inverse distributed load ramp starts and ends somewhere along the beam?

I know how to solve it by moment line methode but i want to use singularity function here and i'm very confused. My strategy consist of writing the correspond singularity function for each element but ...
1
vote
0answers
61 views

How to design a shelving unit out of McMaster Carr Struts? [closed]

I apologize for the complete beginner question. I'm an Undergraduate Research Assistant trying to design a shelving 8'tall by 10' Long, 4' wide shelving unit to support about 200 lbs. I'm designing ...
4
votes
1answer
99 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 ...
2
votes
4answers
128 views

Moment and Torque at a Single Point

As far as I know, moments/torques occur when forces applied are not in line. However, I often see moments/torques being applied at a single point in free body diagrams. How can moment/torque be ...
5
votes
2answers
127 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 ...
1
vote
1answer
2k views

How to find the reaction forces, moments and the displacement of the fixed beam with a link?

The beam is fixed on both ends and there is a link in the middle. There is a force F on the link. My approach to solve this problem: A free body diagram is cut at the link and made into 2 systems. ...
1
vote
1answer
230 views

What is the logic to solve this cantilever problem?

I solved it using the logic that the vertical link of the beam is basically there to make the beam act like a cantilever. So I think it is a cantilever problem. Therefore, $$EI\frac{d^2y}{dx^2}=-px=M$...
1
vote
3answers
90 views

How can the linear relationship between curvature and bending moments be verified?

As part of an experiment, I'm verifying the existence of a linear relationship between curvature and bending moments for three beams using different materials. The plotted data can be seen below. ...
4
votes
2answers
785 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 ...
1
vote
1answer
98 views

IPE Beam weight

In civil engineering calculation I have seen weight of IPE 300 profile expressed in kN/m2 unit. IPE 300 0.42 kN/m2 I know IPE 300 is approximately 42.4 kg/m. How did they calculated that value ...
2
votes
2answers
400 views

Deflection of beam, according to thickness of top plate and bottom plate

When there is one rectangular beam like below image, I would like to know how the beam is deflected according to thicknesses of top plate and bottom plate. My concerning cross section patterns are ...
2
votes
2answers
483 views

Solid mechanics: Deflection of a rectangular elastic membrane

I am trying to solve for the deflection $w$ of a rectangular membrane with tension $T$ acting on two opposite edges. These two edges are fixed i.e. $w = 0$. The other two opposite edges are free. The ...
2
votes
1answer
787 views

Composite beam calculation

I'm building a shelf out of an Oriented Strand Board (OSB-3), reinforced with steel strip attached to it's bottom side. Please check my calculations for deflection. The OSB thickness is $h_{OSB}=18 \...
2
votes
1answer
863 views

Maximum deflection of a beam with both ends fixed and distributed load

I'm designing a part, and I'm trying to figure out what distance a slot should be from the bottom of the part. For simplicity in analysis, I'm approximating the region between the bottom of the slot ...
3
votes
3answers
4k 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 ...
7
votes
1answer
303 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 ...
2
votes
1answer
142 views

Design a beam that is straightened with force on one end

From here, I read that if you have a straight beam, bend it with force at one end, and then create a beam with the resulting curvature, the equal and opposite force won't make a straight beam. What ...
5
votes
1answer
2k 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 ...
4
votes
1answer
1k 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 ...
1
vote
0answers
158 views

Finding My, Mz in Complex/Asymmetrical Beam Bending

So I have done a three point loading test on a piece of bone. I have been able to obtain the Second Moments of Area $I_{xx}$, $I_{yy}$, $I_{zz}$. As well as the centroid. I also have the data from ...
3
votes
3answers
961 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 ...
3
votes
2answers
724 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 ...
7
votes
1answer
1k 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 ...
10
votes
3answers
3k 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 ...
5
votes
3answers
2k 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 ...
3
votes
1answer
3k views

Plotting deflection of a beam

I have a formula to compute the deflection of a beam. When I have computed the deflection I get a vector with non-negative elements representing the deflection in each position on the beam. When I ...
5
votes
1answer
146 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 ...
11
votes
4answers
4k 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 ...