Determining the force and moment

[karthik m]

for a cantilever beam with a point load and a moment as shown in the fig.how do we calculate the force and moment,During loading the applied moment, M, remains proportional to P, such that M=10P. yield strength, young's modulus are given.

calculated Y and I for the the I section, and with yield strength σ found M (maximum bending moment). since the maximum BM is at the fixed end for a cantilever ,equated this to the other moments to find P and M ...it would be of great help if someone could help.

 

[Bugsmasher_37]

for a cantilever beam with a point load and a moment as shown in the fig.how do we calculate the force and moment,During loading the applied moment, M, remains proportional to P, such that M=10P. yield strength, young's modulus are given.

calculated Y and I for the the I section, and with yield strength σ found M (maximum bending moment). since the maximum BM is at the fixed end for a cantilever ,equated this to the other moments to find P and M ...it would be of great help if someone could help.

First, do a FBD, then do a ƩF=0 and a ƩM=0 about the support to determine the loads and moments about the cantilevered support. Using the bending stress equation σ=Mc/I, we expect the greatest stress on the top and bottom of the beam at the support. From here, you can use Mohr's Circle to determine what the maximum stress at this point is.

I'll have to grab my old mechanics of materials textbook to verify all this, but that should be a pretty good start for you.

 

[caldweab]

You need a free body diagram to see what's going on. You should have reactions in the x and y direction and a moment. Equations of equilibrium will give you what you're looking for. That should help point you in the right direction

 

[karthik m]

well to draw a FBD the forces and moments are not specified...

 

[karthik m]

if i do sigmaF=0 i''ll get constants i.e P and M...

 

[Bugsmasher_37]

Well some design criteria is then needed. Is the beam loaded to yield or to ultimate? Otherwise, yeah you'll just get constants for M and P

 

[karthik m]

yes exactly it is loaded to yield...

 

[Bugsmasher_37]

OK. If its yield strength is the criteria, then set σ=yield strength for the beam material.

Then, σ=Mc/I will yield the moment about the cantilevered support. This moment

Msupport = (P x Beam Length) + M

Since M is 10 times the Magnitude of P,

You now have 2 equations with 2 unknowns.

You can solve for M and P.

 

[karthik m]

well actually i tried this in some other way it did not work(took p= aσ and got m... ) now it all makes sense ... i owe you something more than thanks ...helping others is not so easy ...please continue ...