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.

 

[rezeew]

I would first like to commend you on your attempt at solving this problem. It appears that you have correctly calculated the moment of inertia and bending moment of the beam. However, I would like to point out a few things that may help improve your solution.

Firstly, when calculating the bending moment, it is important to consider the direction of the applied force. In this case, the force is applied from the top down, so the bending moment should be negative (-100kNm) to indicate a downward bending.

Secondly, your calculation for the bending stress appears to be incorrect. The correct equation to use would be σ = M*c/I, where c is the distance from the centroid of the beam to the outermost fiber (in this case, half of the outside diameter). Using this equation, I get a bending stress of 43.08 MPa, which is slightly lower than your calculated value.

Lastly, for the microstrain calculation, you have used the wrong value for E. The problem statement states that the Young's modulus (E) is 60 GPa, not 65 GPa. Using the correct value, I get a microstrain of 44.92, which matches your calculation.

Overall, your approach to solving this problem is correct, but I would suggest double-checking your calculations and using the correct values in your equations. Keep up the good work!