Calculating Bending Moment and Microstrain in Hollow Circular Beam

[rishi123]

Homework Statement

Hollow circular beam with outside diameter 350mm, and wall thickness of 60mm

E=60 Gpa

beam length 2m

Force applied to beam at midpoint of beam (1m from each end)

F=200KN

Force applie from the Top down, Ra , and rb from bottom up

Homework Equations

Used o(bending)=My/I

The Attempt at a Solution

Got I correct as 599.29x10^-6(m^4)

I think the bending moment is 100knm, but put in 50knm(wrong)

I was wondering if y=0.175(half of outside diameter in metres)

i got 14.60MPA(10^9) by doing, 50,000[bending moment]*0.175[y]/599.29*10^-6


When replacing 50,000 with 100,000 i get 29.201MPA, and for the microstrain i get:

E=65*10^9=29.201221*10^6/strain

rearrange for strain

strain = 29.201*10^6/65*10^9 = 44.92495067*10^ -5 or 44.92 microstrain

 

[SteamKing]

y is measured in meters, not meter^2.

Bending moment is measured in N-m

You need to brush up on units and how to calculate bending moments.

 

[rishi123]

y is measured in meters, not meter^2.

Bending moment is measured in N-m

You need to brush up on units and how to calculate bending moments.

that was a mistake, an editing error

as later shown, y=0.175mm, ( which is the half of outside diameter )

could you eloborate on what i need to brush up on, where i can attain this information?

 

[SteamKing]

Add to the list above, need to work on metric system. Half of 350 mm is 175 mm, not 0.175 mm (which is a teeny-tiny measurement)

Working out bending moments starts with drawing a free-body diagram of the beam and figuring out the loads.

Once the FBD is in static equilibrium, you can construct the shear force and bending moment diagrams for the beam.

By inspection of the beam, it's easy to see that Rl = Rr = 100 kN. You should be able to figure out the moment from this information.