32
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Accepted
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 ...
- 13k
19
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 ...
- 1,147
16
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 ...
- 21.6k
13
votes
Accepted
Strength of a welded steel gate with vertical bars vs. crossed diagonal bars
As grfrazee said, you won't know for sure until you do a finite element analysis. I was intrigued by this question as a colleague and I got into a discussion about this. While we both agreed the ...
- 1,217
13
votes
Strength of a welded steel gate with vertical bars vs. crossed diagonal bars
Assuming the joints are welded, for the top gate to deform as you draw it the vertical bars will have to bend into an "S" shape. The flexibility in bending will be proportional to the cube of the ...
- 12.4k
12
votes
Accepted
Can I remove one or both of these support posts in my basement?
Whenever one speaks about removing a structural element (column or beam), the initial hypothesis must always be:
NO! GOD NO! WHAT ARE YOU DOING!
The second hypothesis must always be:
No. No. No....
- 13k
10
votes
Accepted
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 ...
- 13k
9
votes
Derivation of beam slope for a cantilever beam
The way to derive the deflection is via the relation $w = EI\dfrac{d^4\delta}{d^4x}$, which means that the deflection is the fourth integral of the loading (and rotation can be taken as the derivative ...
- 13k
8
votes
Buckling: Do buckling mode shapes of n > 1 occur in reality?
If you are looking at the column as being supported at the ends, you are correct that the n=1 mode gives the lowest buckling load.
The other modes (n=2,3,...) aren't useless though. Long columns are ...
- 10.6k
8
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Strength of a welded steel gate with vertical bars vs. crossed diagonal bars
While you've described your problem pretty well, I don't think you're going to find a satisfactory answer without having to run a fairly complex finite element analysis on both structures.
The first ...
- 3,587
8
votes
Accepted
Does the length of a beam change upon deflection?
The dimensions of the beam and magnitude of the deflection are important here. In most structural applications, it's reasonable to assume the length of a beam is unchanged by a small deformation. One ...
- 3,211
8
votes
Accepted
What is the mathematical derivation for shear center of a beam?
SHEAR CENTER
Why do we care?
Because we need to know if the beam is subjected to torsion in addition to flexure.
What is it?
The point in the cross section (or outside the cross section) where we ...
- 2,760
8
votes
Why do we assume the moment is zero when analyzing a simply supported beam?
This rule is typically applied when studying statics. Static means that your structure or object does not move. If the moments didn't all add up to zero, that would mean there was a net force action ...
- 4,511
8
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Strength of a Vertical Round Aluminum Tube with load cantilevered off it?
I'm going to run with this assuming the arm looks like the following diagram (I'm ignoring the 11.4 pounds of the bar for now to make the concepts easier to explain - that can be added later by ...
- 5,323
8
votes
Accepted
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 ...
- 13k
7
votes
Effects of constructed tubular/annular beam upon moment of inertia
Moment of inertia is not a material property, it is a geometric property. Regardless of the material you are dealing with, a member that is 2" wide by 10" tall in cross section has the same moment of ...
- 1,107
7
votes
Accepted
Buckling: Do buckling mode shapes of n > 1 occur in reality?
Whether or not buckling modes with $n>1$ exists depends on how you look at the structure.
As @hazzey notes in his answer, columns with bracing may display buckling modes with $n>1$. These ...
- 13k
7
votes
Accepted
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:
$$W_{max} = \frac{\pi d^3 \sigma}{8L}$$
$\sigma$ ...
- 5,323
7
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 ...
- 12.4k
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 ...
- 7,999
6
votes
Accepted
Why is there a moment at the cross section end when you cut a body?
To put it simply your loads are causing the beam/bar to bend right? So at the cut we need to consider the internal bending moment ($M$).
Like you said: the professor has cut the bar to calculate the ...
- 1,217
6
votes
Plotting deflection of a beam
Deflection
A deflection is a movement in a direction. It is up to you to determine your frame of reference.
It sounds like the calculations that you have done yourself (all positive) are shown for a ...
- 10.6k
6
votes
Accepted
How do you select the correct area to consiser for first moment of area calculations?
You're looking for $\tau_{xz}$, which pertains to horizontal shear flow along the top flange. (Rather than the vertical shear flow considered in $\tau_{xy}$.) As Mark noted, the shear flow starts from ...
- 2,760
6
votes
Does the length of a beam change upon deflection?
Adding to @Air's answer, there's also the issue of boundary conditions. A simple span where neither support allows for axial displacements will have a slight gain in length, including along the "...
- 13k
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 ...
- 1,107
6
votes
Accepted
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.
...
- 21.6k
6
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 ...
- 24k
5
votes
Derivation of the weak form for the euler-bernoulli beam equations
It's easier to understand this identity if you start with the partial differential equation for the Euler-bernoulli beam deflection equation
$$\frac{d^2}{dx^2}\left[ EI \frac{d^2u}{dx^2}\right] = 0$$
...
- 2,539
5
votes
Accepted
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
...
- 21.6k
5
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 ...
- 373
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