# Homework Help: Finding 1st moment of area

1. Jan 5, 2010

### Dell

i am a second year civil engineering student, in mechanics of materials we are dealing with twisting and bending moments and our professor has asked us to think up an experiment in which we can "find" the 1st moment of area of different shapes

this is my idea so far but i need some help developing it
i know that when a beam is subjected to transverse loading, the shear stress in the beam is t=VQ/(Ib) therefore

Q=t*I*b/V

now I, b and V are easy to measure, the problem is finding t (the shearing stress)

what i have thought of doing is using strain gages, stick them at a point at which i know the internal shearing stress V, but im not quite sure how to measure the SHEARING stress using the strain gage, had it been the normal stress i could have used youngs modulus to find the stress through the normal strain, or using a strain rosette(dont think its necessary)

can anyone improve on this or even think of a better way- it doesnt necessarily need to have anything to do with bending and twisting.

2. Jan 5, 2010

### Dell

o sorry, i can use the strain rosette to find the shear strain and then multiply by 2G to find the shear stress, but how do i set up the rosette since i want to measure at a cetrain point(lets say at the centroid of the beam) how would i place the 3 strain gages? since they are not so small that they will measure my strain ONLY at the center where the shear strain is maximum, - i am working with a regular rectanglular cantilever

another problem i have is how to stick them, since anywhere on the front exposed edge the shear strain will be 0 since there will be no internal shear force?

3. Jan 5, 2010

### Dell

could i take 2 beams, stick the strain gages on the top of one and then glue them together somehow?

4. Jan 6, 2010

### Dell

this is my basic idea, can someone tell me if it should work and if there are any problems you can see

i place strain gages on the cantilever beam near where x=0, and the bending moment is F*L

now i use a strain rosette at 45 degrees to measure the strains at x y and 45
through this and using the deformtion equations i can find the xy shear strain

using hookes laws i can now find the xy shear stress and through t=VQ/(Ib) i can find Q

5. Jan 6, 2010

### PhanthomJay

Heck, I don't know, what a strange way to determine (presumably) the first moment of the area above (presumably) the neutral axis, when for a rectangular soild cross section of width b and height h, it's simply Q = area above neutral axis times distance from centroid of area to neutral axis = (bh/2)(h/4) = bh^2/8. I don't get the purpose of the experiment.

6. Jan 6, 2010

### Dell

that i cannot tell you, i agree, but that is what we were asked to do- fthink of an EXPERIMENT to fint the moment, not use the equation,
will this work?

7. Jan 6, 2010

### PhanthomJay

Sorry, I don't know that much about shear strains and strain gages. I can tell you that the e-xx strain will be 0 at the neutral axis, since ther is no bending stress there; also, in determining the value of Q, knowing the shear stress, you have to use the equation anyway! And also, the shear stress distribution is assumed constant across the width of the beam at a given line parallel to the neutral axis, which is not necessarily true, so your results are going to be off.

8. Jan 6, 2010

### Dell

e-xx will be 0, as well as e-yy will it not?? but thats just the formality i used because thats the equation, so i will find e-xy=e1/2

9. Jan 6, 2010

### PhanthomJay

I don't know, I'd have to read my 40 year old textbook to find out, since I've never used shear strain equations (only shear stress equations) in my line of work. I still don't like the experiment; it 's sort of like taking a 2 x 2 square section and finding its area by a applying a tensile load, T, to the member, calculating the stress using strain gauges, then using A= P/stress to find the area. I suppose if it was an irregular shape, that might be of some benefit, but in calculating Q of an irregular shape using your method, you still need to calculate I, so that requires a geometric knowledge of the member cross section. Maybe there's another experiment you can do besides using strain gauges (I can't think of one)? Seems weird to me.