Finding Maximum Positive Moment and Negative Moment in Mathcad of M(x)

[CWEngineer]

I have a function M(x) which is the moments in Mathcad. Do you guys know how can I determine the maximum negative and positive moment value from this function. Thanks

 

[Lion06]

Yes.
Write another equation setting dM/dx=0. This is essentially telling you the locations of zero slope (which is maximum moment).

 

[CWEngineer]

How can I set up the process so that I can get as output the max posive and max neg moments including the endpoints. Thanks

 

[Lion06]

I don't use mathcad, but I am assuming you know how to do the setup. I am just telling you that if you already have the M(x) function, that the derivative of that function, dM/dx, will tell you the maximum moments in your M(x) function. Whenever you have dM/dx = 0, you have a maximum (or minimum) moment.
Additionally, I would be surprised if mathcad didn't have a max/min function that you could pull out the max/min moments from your M(x) function.

 

[frv]

StrEIT-


That would only work with distributed loads for a simply supported structure. It would also fail for a cantilever.

 

[Qshake]

There is a MathCAD forum here, look for PTC: Matcad.

Once you have the values for the function, M(x) you should be able to use MaxM(x) and MinM(x).

Addiitonally you should be able to easily plot the function using Alt F2 (?) to see if what you're getting for M(x) is acceptable for your configuration.

Regards,
Qshake

Eng-Tips Forums:Real Solutions for Real Problems Really Quick.

 

[Lion06]

frv-
I am not sure I agree completely. The shear is the derivative of the moment. This is why the max moment occurs where the shear diagram changes from positive to negative (regardless of whether it is a uniform load or some series of point loads and uniform loads).
For the same reasons, the moment of a beam at a point is the derivative of the slope of the beam at that point. If the slope is zero (as would be the case for a cantilevered beam at its support), then that is where the moment is maximized (from an absolute value standpoint).
In the case of non-uniform loading you will need more than one equation for the moment function, M(x), but the principle is the same. I'll think about this a little more........ I have to run out for a while.

 

[JStephen]

Check where dM/dx = 0 as above, but also check the endpoints and any point where a load or support occurs (IE, points where there is a discontinuity in the shear function).

 

[frv]

strEIT-

Think abut a point load at midpoint of a simply supported beam. The moment diagram is a triangle with the apex at midspan. The derivative of the moment has only two values- one the line going from the support to the apex and the second from the apex to the other support. The derivative at the point load is undefined.

With a cantilever, depends on the load, but say you have a distributed load. The derivative of the moment will be maximum at the support. For a point load, it would be constant from support to the point of the load.

 

[asixth]

gman1,

I wrote a simple frame analysis routine in Matlab that I assume would be very similar to MathCad. For each element, I have an equation for shear V(x) and an equation for moment M(x), like StructuralEIT writes, to find the maximum moment of an element, you need to calculate where the shear force equals zero, for a beam-element in a frame, this will occur at both supports and somewhere midspan (that is x=0; x=~0.5L; x=L). Once you calculate the position x, you can substitute this into the M(x) to calculate the maximum moment.

I would also investigate into the tools of MathCad, there may be a function that allows you to calculate the max and min values for a given function.

If you are using MathCad for a similar reason that I am using Matlab, then you should only be concerned about the maximum mid-span value, the negative moments at the support are easy to find.

 

[UcfSE]

Use a solve block and the maximize function.

M(x)=wLx/2-wx²/2


x:=1 (have to enter a guess for the solver)
Given (not as text)

enter constraints, such as x>0 and x<L

x_max:=Maximize(M,x)

Check the help section for more information. I'm sure there are several ways of accomplishing this.

 

[NS4U]

attached your mathcad sheet... it will make showing you how to do this easier