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32 votes
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Why is this bridge thickest above the support pillars instead of the mid-span where the bending stress is highest?

If I model this as a simply supported beam having load at mid span [...] I suspect that this is where your analysis went awry. First off, you should always model bridges with distributed loads, not a ...
Wasabi's user avatar
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20 votes

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

While not an ideal situation, it is common enough that this type of cut/reduction of the beam as it comes to its support actually has a name. This is more often referred to as a coped or dapped steel ...
Forward Ed's user avatar
  • 1,221
17 votes

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

This is a textbook example of what not to do. We don't get into stress concentration at the cut off of the corner of the beam, or the fact that the two very different stiffnesses of the beams are a ...
kamran's user avatar
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10 votes
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Why does a continuous beam have less deflection than a pair of simply supported beams?

For a simple visual demonstration, take one of the spans in your example. If it is fully hinged, then each span can be represented as a simply-supported beam. If the beam is continuous, then each ...
Wasabi's user avatar
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8 votes
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Stiffness of a cantilever beam

Stiffness is a murky term frequently used ambiguously in engineering. However, the most common definition of stiffness is the product of a beam's Young's Modulus $E$ (which is a function of its ...
Wasabi's user avatar
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8 votes

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

If the white beam on the left is adequate, the one on the right is much bigger than it needs to be, so hacking a piece out of it might not matter. In general this idea is a horrible example of ...
alephzero's user avatar
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7 votes
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Given the tensile strength of a rod, how do you calculate the max weight that can be hung from it?

You're hanging it from a rod supported by both ends - and need to use the bending equations. For this case (case 7 in the link), the max weight is: $$W_{max} = \frac{\pi d^3 \sigma}{8L}$$ $\sigma$ ...
Mark's user avatar
  • 5,333
7 votes

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

TL;DR: Since we can't see how the beam is supported on the other end, its not clear whether its structurally safe. Still, I don't believe this configuration can transfer safely any substantial ...
NMech's user avatar
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7 votes

Why is this bridge thickest above the support pillars instead of the mid-span where the bending stress is highest?

Since this bridge is crossing over a waterway, besides aesthetics, the arch-shaped bridge provides several advantages: Less restrictive over the height of marine traffic due to more headroom in the ...
r13's user avatar
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6 votes
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How much weight can an aluminum tube beam support?

We use this equation for a simply supported beam loaded at its center with 200lbs. M= P x L/4 =200 x 3 /4 = 150 lbs.ft for calculating the tube stress we convert this to 150 x 12 = 1800 lbs.inch ...
kamran's user avatar
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6 votes

Determining stiffness of a beam w/varying moment of inertia

You could insert the variable $I(x)$ into the integral equation for the rotation and the deflection. First determine your model. Then determine the equation of the moment $M(x)$. Then enter this in ...
jos's user avatar
  • 393
6 votes

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

This means that the member is considered to be fully loaded for a failure mode which is being analyzed by that stress calculation. Some things to (probably) keep in mind include: Some conservatism ...
William S. Godfrey- S.E.'s user avatar
6 votes
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Deflection of a cantilever beam composed of separate (not bonded) planks

in a cantilever beam the deflection is $$\delta_{max} = \frac {PL^3}{3EI} $$ In this case assuming free sliding between the planks the load P is going to be supported equally between the 3 planks. ...
kamran's user avatar
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5 votes
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Are the points of inflection and contraflexure the same?

A point of inflection is defined as the point where a function changes from convex to concave or vice versa. For a function $f(x)$, this is frequently mathematically defined as the point where $f''(x)...
Wasabi's user avatar
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5 votes
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Why are steel I-beams mostly symmetrical?

Academically, I believe you are correct in that you could potentially optimize an I-beam to have a higher failure-load to mass ratio. You would have to play with the area moment of inertia equations ...
ericnutsch's user avatar
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5 votes

Timoshenko Beam Theory for Quasistatic Cantilever Beam: Shear Term

Timoshenko originally solved the equation with a $k$ factor. The $c^2$ factor came as a result of Timoshenko's analysis. The goal was to keep $k$ as a constant, which would make the equations easier....
Mark's user avatar
  • 5,333
5 votes

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

So, we apply a point load to the end of the cantilever beam and can see that for external equilibrium, there must be shear reaction at the support. (Leaving aside for now the moment reaction that also ...
CableStay's user avatar
  • 2,760
5 votes
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Do internal / external stresses affect modal frequency?

Consider a small piece cut out of a structure that has non-zero internal stress. To maintain equilibrium, there must be some forces applied to the boundary of the piece. (Of course when it was part ...
alephzero's user avatar
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5 votes
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Degrees of freedom of an internal hinge in plane beam?

Let's start talking not about hinges, but supports. Specifically, why do supports generate the forces (including bending moments, if applicable) they do (or don't)? Think of a simply supported beam ...
Wasabi's user avatar
  • 13.1k
5 votes

Limits of Euler-Bernoulli Beam Theory for Wide Plate in Flexure?

For a rectangular simply supported plate with length $a$ and width $b$ (Roark's Formulas for stress and strain): $$\sigma_{max} = \sigma_b= \frac{\beta qb^2} {t^2} $$ $\beta$ ranges from 0.287 for a=...
kamran's user avatar
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5 votes
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Beam buckling criterion?

Shear buckling of beam web happens when the shear at a section of the beam under consideration surpasses the controlling combination of factored shear. The following three equations are the LFRD ...
kamran's user avatar
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5 votes
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Why is it said that the flange of an I beam carries most of the moment?

What is really proportional to the distance from the neutral axis (let's denote it $z$) is the strain. For pure bending and a symmetric cross-section the equation for strain is given by $$\epsilon(z) ...
NMech's user avatar
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5 votes
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What are the units used in beam bending equations? Do they matter?

Yes, the equations are valid for both imperial and metric systems. The most important thing is to use consistent units of a system throughout the calculations. Consistency of units matters as most ...
r13's user avatar
  • 8,202
5 votes
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Rigidity and bending moment

Yes, a rigid beam can contain bending moments (as well as any other internal forces). Stiffness affects how an element deforms, not its capacity to resist forces. In isostatic (statically determinate) ...
Wasabi's user avatar
  • 13.1k
4 votes

Does the length of a beam change upon deflection?

A subtle bit of wording - the exact length does not change, as pointed out by Air above in his answer. However, the horizontal projection of the beam does change, as the shortest path between two ...
Mark's user avatar
  • 5,333
4 votes
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Round beam deflection under its own weight

No, as the Wikipedia article states, a uniform load's unit is in "force per unit length" ($F/L$), which means it is a load applied along a given distance. So, if you have a 102 g beam, it weighs ...
Wasabi's user avatar
  • 13.1k
4 votes
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Reinforcing beam and slab with correct steel bar structure

Model 1 is always better, but may need some modifications Whenever you have two reinforced concrete elements, you always need to facilitate the transfer of internal stresses between them. This is ...
Wasabi's user avatar
  • 13.1k
4 votes

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

There are two basic types of structure. Statically determinate structures are those where you can calculate the forces at the restraints without knowing anything about the flexibility of the ...
alephzero's user avatar
  • 12.5k
4 votes

Buckling vs. Yielding Failure of Columns

The basic Euler buckling formula is unrealistic because it implies perfect geometry and perfect alignment of the loads. Therefore a large empirical safety factor is required. It is also a potentially ...
alephzero's user avatar
  • 12.5k
4 votes

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

The lower flanges resists a downward bending force that puts tensile stress on the lower flanges. Removing a short section of the lower flange lowers its bending strength but because of the very short ...
blacksmith37's user avatar
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