7
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.
...
- 21k
6
votes
Why does a simple pin-ended triangular (arched/curved) beam deflect more due to secondary effects (non-linear analysis)?
Play around with a simple version of this structure, made from a sheet of paper fixed in a slight curve, and see what happens when you apply a load to the mid point.
If the first example, any ...
- 12.5k
5
votes
Accepted
Where is the axis of bending for a box lifted by a crane?
If by axis of bending you mean box functioning as a beam and also the top and walls and bottom of the box are integrated and work like a hollow rectangular beam, then the neutral axis is at the mid ...
- 21k
5
votes
Accepted
Why does rebar in reinforced pre-stressed conrete reduce in deflection if compressive stress is applied to member?
Prestress creates an upward deflection on the beam due to the combination of elastic strain, creep and shrinkage in the unloaded beam.
This negative deflection will bend back to a straight stance or ...
- 21k
4
votes
Breaking strength of stainless steel bar
There are a number of unknowns in the problem statement:
The geometry of the bar
The location of the supports
Whether the beam is simply supported or clamped at these supports
Whether the load is a ...
- 1,428
4
votes
Accepted
Structural Frame Real World Deflection
Yes the left column would deflect in the real world. The reasons are:
1) Eccentricity of the connection / column:
In reality the load will not be transferred perfectly to the center of the column ...
- 2,631
4
votes
Accepted
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 ...
- 13k
3
votes
Deflection of a cantilever beam composed of separate (not bonded) planks
Thanks to @kamran for his answer.
I simulated the problem in ANSYS student v19 to verify his approach.
In the pictures below, the upper beam is solid, the middle one is split into two segments and ...
- 448
3
votes
Why does a simple pin-ended triangular (arched/curved) beam deflect more due to secondary effects (non-linear analysis)?
The answer of alephzero is spot on. I just want to mention that the arch structure is particularly sensitive to 2nd order effects when it is shallow (say depth to span ratio ~0.1) . It's not ...
- 347
3
votes
Accepted
Deflection of thin plate with 1 free edge and deflection > thickness
You are correct that this problem falls within the category of 'large-deflection' problems since the deflection is larger then about $\frac{t}{2}$. To correctly analyse a plate under large-deflections ...
- 2,631
3
votes
Accepted
How to calculate deflection of a cantilever beam subject to point loading
Both answers are incorrect.
Your answer to (a) would imply that the bending moment is equal to zero at $x=0$ and increases linearly until $x=L$. This is only true if you put $x=0$ at the free end of ...
- 13k
3
votes
Accepted
How is shelf deflection determined?
The exact deflection result is a function of the shelving's structural system. In the OP comments you mention that the two options would be either a wooden skin with metal edging or a wooden lattice ...
- 13k
3
votes
Accepted
What is the effect of end diaphragms on prestressed girder forces/deflections?
I have no resources to point to in regards to this, but I'm fairly certain your gut-feeling is correct. In fact, end diaphragms exist in bridges primarily to hold the soil on the approach. They can ...
- 13k
3
votes
Maximum deflection of a beam with both ends fixed and distributed load
You need to decide whether the design limitation which determines h is max stress or max deflection.
If you decide deflection is more important insert the value for y which is the maximum allowable ...
- 15k
3
votes
Why does rebar in reinforced pre-stressed conrete reduce in deflection if compressive stress is applied to member?
Concrete is strong in compression but weak in tension. In tension, it will crack at a much lower stress than the allowable compression stress.
A reinforced concrete beam without any prestressing will ...
- 1,278
3
votes
What plastic material is best for a snap-fit design?
I have designed parts which are snap-fit using Polypropylene. They work well, but the best advice I can give make one (or a few) in one or more material and do some life testing to figure out which ...
- 1,806
2
votes
Should long-term prestressed girder camber always be upward?
The questions in your title and in your body-text are slightly different.
Prestressed girder camber should usually be upwards. This is because one usually applies sufficient prestressing to cancel ...
- 13k
2
votes
Deriving the deflection force equation for a beam that is fixed on both ends
Consider a horizontal beam of length $L$ along the x-axis with vertical displacement $v$. Also consider that is has an applied load $P$ at $\frac{L}{2}$:
$$\dfrac{d^2v(x)}{dx^2} = \dfrac{M(x)}{EI}$$
...
- 1,217
2
votes
Accepted
Undesired vibration of a beam under foot traffic
An exact theoretical analysis of this is rather involved so I will take an approximate approach.
We can idealise the beam as a single degree of freedom (SDOF) dynamic system. The theory behind this ...
- 2,631
2
votes
Accepted
What is the formula for deflection of an end-loaded cantilever rod beam?
For a cantilever with a point load at the free end, the deflection at that free end is:
$$\dfrac{WL^3}{3EI}$$
Handbook of Structural Steelwork - 3rd edition
where
$W$ = point load
$L$ = beam ...
- 3,135
2
votes
Accepted
Bending equation and max deflection of UDL and multiple point loads
Note: I'll be using the following notation:
$q_1, q_2$ are the distributed loads (where you use $w$, which I reserve for deflections)
$L = c + 2(a+b)$, the total length of the span
$\ell = a + b$
I'...
- 13k
2
votes
Deflection of a stack of disks under applied force/pressure
Between disc 1 & 2, there is a reaction force on disc 1 which is not going to act on the edge rather at the distance of 2nd disc edges.
This means you need to have the model of 1st disc bending ...
- 21
2
votes
Deflection of a cantilever beam composed of separate (not bonded) planks
Although I agree with @kamran, I have another way of thinking about it
The deflection of the structure is
$$\delta=\frac{P\cdot L}{3\cdot E\cdot I}$$
The only difference in this problem between then ...
- 22.7k
2
votes
Accepted
Why do we increase the minimum beam/slab depth if we increase the grade of the reinforcement to control the deflection
The principle behind that table is that you will be doing a strength calculation in any case and need the table for a guideline of whether deflections or bending strength will be the design driver. ...
- 1,278
2
votes
FEA: What is the difference between a spider of RBE2s and multiple SPCs
... the spider is the more accurate method as multiple SPCs make the model
overly stiff ...
That depends what you are trying to do. Remember that (1) the RBE2 does not have to connect to all 6 DOFs ...
- 12.5k
2
votes
Deflection In Multistory Structure
In US, The American Society of Civil Engineers (ASCE) Structural Engineering Institute (SEI) publishes Minimum Design Loads for Buildings and Other Structures (ASCE/SEI 7-10).
Section 12.8.3 Vertical ...
- 21k
2
votes
How can I find deflection in a member that doesn't have a constant area moment of inertia?
There are two aspects to this problem that are each significantly more complicated than what you seem to have tried so far:
The angle of 45 degrees by which the cross section is changing dimension is ...
- 1,278
2
votes
Castigliano's theorem for deflection
It is because of the boundary condition - point B is fixed against deformation, so if you apply the load at point B, it results in zero strain, thus zero energy.
- 7,624
1
vote
Deflection of a stack of disks under applied force/pressure
The Radius of curvature on a beam bent under moment is $1/r = m/EI $
If we use this just as a rough model the m affecting each disk gradually becomes smaller as we go up and radius of curvature ...
- 21k
1
vote
Which diameter and thickness pipe to choose
10kg of cover on roughly 10kg worth of pipe? Never mind moist environment where rust will be a serious problem... never mind if you intend it to roll by crank (like in the PDF attached), in the ...
- 6,133
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