Support Types and Their Reaction Forces
Support Types and Their Reaction Forces
(OP)
Hello all
Please dont shoot me down for asking this question as I know it maybe simple for most people.
I am trying to remove doubt from my mind regarding the 3 x types of supports and their reactions.
To me the types of support and their reaction forces are:-
Fixed Support = Vertical Reaction, Horizontal Reaction, Bending Moment Reaction.
Hinged Support = Vertical Reaction, Horizontal Reaction.
Roller Support = Vertical Reaction, Bending Moment Reaction.
To me the above supports can ONLY have those reaction forces - would this be correct?
The reason I ask is because someone told me that a roller support does NOT have a bending moment reaction and i was immediately thrown into confusion.
Can anyone confirm?
Thank you.
https://files.engineering.com/getfile.aspx?folder=...
Please dont shoot me down for asking this question as I know it maybe simple for most people.
I am trying to remove doubt from my mind regarding the 3 x types of supports and their reactions.
To me the types of support and their reaction forces are:-
Fixed Support = Vertical Reaction, Horizontal Reaction, Bending Moment Reaction.
Hinged Support = Vertical Reaction, Horizontal Reaction.
Roller Support = Vertical Reaction, Bending Moment Reaction.
To me the above supports can ONLY have those reaction forces - would this be correct?
The reason I ask is because someone told me that a roller support does NOT have a bending moment reaction and i was immediately thrown into confusion.
Can anyone confirm?
Thank you.
https://files.engineering.com/getfile.aspx?folder=...
RE: Support Types and Their Reaction Forces
RE: Support Types and Their Reaction Forces
RE: Support Types and Their Reaction Forces
RE: Support Types and Their Reaction Forces
Of course this is statics at its most basic level. In reality you have to look at it in 3 dimensions, with reaction forces in all three axes and reaction moments about all three axes. Then you have partial fixity, spring supports, etc.
RE: Support Types and Their Reaction Forces
The concept should not cause confusion...Fixed, Pinned, Roller = 0, 1 and 2 degrees of freedom respectively.
BA
RE: Support Types and Their Reaction Forces
Thank you for your responses, I really appreciate it.
Just a follow on question.
The attached drawing (Picture 1) shows a member that support a UDL of 200kN.
The member sits directly on 3 x supports, to me I would describe these supports as roller supports?
If this is correct then they have no horizontal reaction forces which I am happy with.
However since it is a roller support it has no moment reaction but I struggle to visualize this, the flat underside of the member sits directly on a flat horizontal supports - would it be correct to say that the the member rotates about the edge of the supports as shown in picture 2 (forgive my poor sketch, I have highlighted in red circles the rotation points).
https://files.engineering.com/getfile.aspx?folder=...
https://files.engineering.com/getfile.aspx?folder=...
Thank you.
RE: Support Types and Their Reaction Forces
1) All 3 are pin support - this is correct if the member is connected to the support beams through positive fastening.
2) All 3 are roller support - this is acceptable for gravity load only, provides the member is not positively connected to the support beams, and having frictionless medium in between the member and the supports(note this type of support specification violates the rule regarding global stability - the member can move horizontally, but will not affect the analytical results).
Regarding your second question: Theoretically the member will rotate about the centroidal axes. Your sketch depicts the deflect shape of the member with 3 roller support - the supports do not rotate with the member. For the member support on 3 pin supports, at least the outer two supports will rotate with the member, because of the drag force from the connections and shear friction.
RE: Support Types and Their Reaction Forces
BA
RE: Support Types and Their Reaction Forces
I just wanted to point out the load description (UDL) and the units of the load (kN) do not agree with each other.
Regarding to the 3 rollers system, it is unstable, so theoretically there is no solution, and in reality, no one shall do it. But strictly speaking, in a limit equilibrium situation without any cause for lateral movement, the vertical reaction under each support is identical to that obtained for a stable system.
The image below compares results from the 3 pins system, and the system with 1 pin and 2 rollers. No warning was issued from the program.
RE: Support Types and Their Reaction Forces
BA
RE: Support Types and Their Reaction Forces
Everything BAretired has added in his last 2 posts is correct here
RE: Support Types and Their Reaction Forces
Most likely, the beam was modeled as being rigid or very stiff. No bending = No deflection = no change in the length of the beam = no horizontal forces.
Rod Smith, P.E., The artist formerly known as HotRod10
RE: Support Types and Their Reaction Forces
To be precise and clear, the conventional description of the loading on the OP's example should be:
- ..the beam has a total load capacity of 200kN, that is uniformly distributed over..., or
- ..the beam supports an UDL of XX kN/m in metric system, or XX plf/klf in the US system.
TO Agent666,
You have raised an important question, though it is not in the OP's query.
I think in general purpose structural analysis, the program ignores the secondary effect, that produces horizontal reaction at pin support. Evident by another examples below - left end fixed, right end on roller, or pin support. A person familiar with structural programming should be able to point out why, or RISA has committed a mistake.
We know in reality, secondary effect shall be included to obtain true reactions afford by the pin support, that is important in design of the connection. Also, in reality, for beam over multiple supports, imo, should be modelled as beam supported by multiple pin supports, unless there is clearly no physical horizontal restrain at the interface, which is rare.
I guess the OP is in the elementary level of structural analysis and design. Wish he/she has knowledgeable mentor around, and study more.
RE: Support Types and Their Reaction Forces
That has been demonstrated in a thread fairly recently (I forget the name of the thread offhand). Simply extend the rule to a beam, whether simple or continuous. Use at most one pinned support. It doesn't matter which support is pinned. The remainder should be rollers if you want to be sure the results are accurate.
In the case of cable, it's a different story. The cable has an initial sag and the supports must be able to resist the horizontal component of the cable.
BA
RE: Support Types and Their Reaction Forces
That statement is completely wrong, hence very bad advice to give to a young engineer reading this thread. It may be true for some software, I don't know, but it is theoretically incorrect. If the pin supports are placed at the bottom of the beam, where I would expect them to be, all pins are located h/2 below the beam's neutral axis, where h is the height of beam.
In the case of a simple span, the bottom fibres are in tension across the full span. If the ends are pinned, how can that be? A pin at each end means there is no change in length.
BA
RE: Support Types and Their Reaction Forces
I'll let the sketch speak itself.[Sketch was withdrawn and revised]RE: Support Types and Their Reaction Forces
Your sketch speaks with forked tongue.
When pin supports are placed at the bottom of the beam, they must resist a horizontal reaction. If there is one pin and the remainder rollers, there can be no horizontal reaction. See simple span at the left in sketch below for support location. The bearing point of a pin or roller is not at the neutral axis of the beam. It is usually at the bottom as you show on Sections 1 and 2.
Try relocating your pin supports h/2 below the neutral axis by using a rigid extension from the neutral axis down to each pin and let us know if you get horizontal reactions.
BA
RE: Support Types and Their Reaction Forces
Rod Smith, P.E., The artist formerly known as HotRod10
RE: Support Types and Their Reaction Forces
Unfortunately it's telling lies, that picture is wrong in the sense that if you apply a concentrated horizontal load to the end of the beam at the support location as shown in the bottom picture with 4 pins, all of the H load is resisted by the first pin supoort. The beam doesn't distribute the load to all four pin supports as implied.
You don't need a computer analysis, just some basic understanding of statics (usually 1st year stuff at University) to follow the logic.
Exactly.
RE: Support Types and Their Reaction Forces
RE: Support Types and Their Reaction Forces
Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?
-Dik
RE: Support Types and Their Reaction Forces
If it's a roller, there can't be something horizontal or it would roll.
BA
RE: Support Types and Their Reaction Forces
You have not responded to my suggestion that pin and roller supports are at the bottom of the beam, not at the neutral axis.
For a simple span beam with uniformly distributed load, the end rotations can easily be calculated. If the rotation at each end is θ, the total strain of the bottom fibre is 2yθ where y is the distance between the neutral axis and the bottom of beam. If a pin support is used at each end, the total strain must be zero.
I suggested a way you can check that with your software, but you have simply ignored the suggestion. You seem to be more interested in clouding the issue than seeking the truth.
BA
RE: Support Types and Their Reaction Forces
RE: Support Types and Their Reaction Forces
I don't know why you can't discuss this in a civilized manner. And I don't need software to carry out my suggestion!
BA
RE: Support Types and Their Reaction Forces
With all due respect and in a civilized manner:
What should be included in secondary effects? How about temperature change? Is that a secondary effect? If multiple pin supports are modelled, the beams cannot change in length, causing axial forces throughout the beam and horizontal reactions at some supports.
Continuous beams do not always have the same cross section in every span. Even when they do, placing pin supports at the bottom of a beam, instead of at the neutral axis, causes horizontal support reactions which alter moments and axial loads throughout the beam.
This can be avoided by using one pin support, and the rest roller supports. Alternatively, by using horizontal roller supports at every location and adding one vertical roller support anywhere to provide stability to the structure. That would be my recommendation, contrary to the red text in the above quote.
BA
RE: Support Types and Their Reaction Forces
RE: Support Types and Their Reaction Forces
Exactly, BART...
Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?
-Dik
RE: Support Types and Their Reaction Forces
Honestly unsure where you are trying to go with your argument, are you just taking the piss and winding everyone up on purpose by posting the incorrect information repeatedly? If so you should stop, it isn't adding to the original intent of the post.
RE: Support Types and Their Reaction Forces
RE: Support Types and Their Reaction Forces
Maybe you are looking at things differently. I do not believe, and do not suggest that you are intending to mislead anyone. However, I am not following your latest diagrams.
Below is a sketch of a two span continuous beam. The upper diagram has three pin supports located at the bottom of the beam. The lower diagram has one pin support and two rollers. The loading is the same for both diagrams, namely a UDL over both spans and a couple of sloping forces on the right hand span represented by sloping arrows.
An analysis of these beams will yield different results for shear, bending moment and axial load because the boundary conditions are different. We can discuss these differences in more detail if anyone wishes. The second diagram is the arrangement I suggested, but the location of the pin support can be moved to either point b or c if preferred.
BA
RE: Support Types and Their Reaction Forces
RE: Support Types and Their Reaction Forces
Your program is representing the beam as a single line with supports at the same level. In effect, that means your supports are at the neutral axis of the beam. You need to drop the pin and roller supports by half the beam depth to see a difference in the shear and moment diagrams. This means adding nodes N4, 5 and 6 at an elevation one foot (or half the beam height) below N1, 2 and 3 with three infinitely stiff vertical members fixed to the beam from N1 to N4, N2 to N5 and N3 to N6.
BA
RE: Support Types and Their Reaction Forces
Your suggestion/request is beyond the realm of elementary/general structural analysis, that considers all applied and resultant forces are acting on/about the centroid of the member; similarly, the support is located at the intercept of its axes and the centroid of the connected member, not the extreme fiber of the physical beam. You may try yourself the model as you suggested, and post the findings. I am eager to learn the difference, but don't know how to properly handle the modeling in a general purpose structural analysis program such as Risa2D. Sorry.
Note: There is a "member offset" commend in STAADPro, maybe that is something you are interested in. Haven't use the program for a longtime, so really can't provide information on how it works.
RE: Support Types and Their Reaction Forces
The simplest frame is a single portal frame which can easily be analyzed by any 2D frame program. Multiple bay frames can also be analyzed by the same software.
When a single span beam is analyzed, it is usual to consider supports to be one pin and one roller. There is a good reason for that. If two pins are chosen as supports, the assumption of all forces acting at the centroid of the member cannot be achieved in a real structure because the pins are usually located at the bottom of the beam rather than at the neutral axis.
I am proposing to consider a single beam as a portal frame as shown below where the distance from the neutral axis down to the pin is 'h'. I will assume that I2/I1 = 1, although it should be much smaller.
k = h/L and N = 2h/L + 3
Mb = Mc = -wL^2/4N = WL/4N where W = wL
Ha = Mb/h = WL/4hN
If L = 20'-0" and h = 1'-0",
then N = 5 and Mb = Mc = WL/(4*5) = WL/20
and Ha = WL/20*1 = W
The assumption of pin supports, using this method, produces significant end moments on the beam as well as a substantial axial compression.
If one of the pin supports is changed to a roller, the end moments and the horizontal force Ha both vanish.
That is interesting and may be another good approach to the problem. I do not have STAADPro, however and can't justify purchasing it under the present circumstances.
BA
RE: Support Types and Their Reaction Forces
This is the mean difference of us. I do recognize your concern. In practice, we model according to member centroidal axis, and put support on the same level. If the perceived effect (I call it secondary effect) is large, we perform hand calculation (ie. Ma = H*d/2), or use member offset comment, and impose the load on the support. It is just something needs to be designed for, because in real structure the supports are most likely connected to the member above.
The structural models below show the typical way of modelling.
RE: Support Types and Their Reaction Forces
RE: Support Types and Their Reaction Forces
then k = 0, N = 3
and Mb = Mc = WL/12 or wL2/12 (a fully fixed end)
Ha = Mb/h = WL/12h
So the elevation of pin supports makes a huge difference in the result.
That is why we use pin and roller for a simple beam, rather than two pins.
BA