Need to find 2nd moment of area

[clot67]

Hi all, i m new here, been given a task to find bending stress σ when force F is applied, the figure can be model as a cantilever, the support is on the left.,but i don't know how to find 2nd moment of area (I) for the figure below, pls help
thanks in advance.

Homework Statement

Homework Equations

σ=(M(T/2))/I

The Attempt at a Solution

 

[pongo38]

First, you need to give us a clue as to how far you can get. Second, the figure is not totally clear. On the top left figure, which is presumably a plan, where exactly is F applied? Is it a point load or a knife edge load along two edges? Thirdly, can you identify the cross-section whose second moment of area you want? Finally, what definition do you know for I?

 

[clot67]

First, you need to give us a clue as to how far you can get. Second, the figure is not totally clear. On the top left figure, which is presumably a plan, where exactly is F applied? Is it a point load or a knife edge load along two edges? Thirdly, can you identify the cross-section whose second moment of area you want? Finally, what definition do you know for I?

i m not sure the load is a point load or knife edge. i assume it should be knife edge. i forgot which cross-section area i should be finding for. i know i mus use (bh^3)/12 but i don't know what is my b and what is my h.

based on the forumla σ=(M(T/2))/I, my h should be T and b should be A but the cross-section area is not uniform. i m confused now. pls point me in the right direction.. thanks

 

[pongo38]

It's not your fault that it is a badly worded question. If the support is at the left end, then it looks like A is the span. At the root of the cantilever, b is the C on the drawing. Further towards the load, it is C-D. You are correct that T is the h you are looking for. Perhaps you have to look at both sections to find which stress is maximum. It would also depend on whether F was shared between the two prongs of the fork. You are correct that I = use (bh^3)/12 where b is parallel to the neutral axis in the cross section and h perpendicular to the neutral plane...

 

[DeeNos]

Hello, welcome to the forum! The second moment of area (I) is a geometric property that represents the distribution of an object's cross-sectional area around an axis. It is also known as the moment of inertia or the area moment of inertia.

To find the second moment of area for your figure, you will need to use the formula for the moment of inertia for a cantilever beam, which is I = (1/12)bh^3, where b is the width of the beam and h is the height. This formula assumes that the beam is rectangular in shape.

Once you have calculated the second moment of area for your beam, you can then use the bending stress formula you provided, σ=(M(T/2))/I, to find the bending stress at the point where the force is applied. M is the bending moment, which is equal to the force (F) multiplied by the distance (T) from the support to the point where the force is applied.

I hope this helps! Let me know if you have any further questions. Good luck with your task!