# Transverse Shear Stress

Transverse shear stress is a bit of For most students to understand the equation is VQ over ip V is the Shear Force Q is the first moment of area? I is the inertia and t is the thickness of the material at the point you are examining this is different from the average shear stress equation which is V over a this equation is used to identify the shear stress at a specific point and The maximum Transverse shear stress occurs at the neutral axis the basis behind VQ Ip Is to look at the how the bending stress works out when you look at your cut you will see a shear force and a moment reaction But when you look at the stress distribution from the bending moment you’ll notice that it is creating off opposing stress distribution across the cross section So if you make a cut like this, you will notice that there must be a shear stress on the bottom face Knowing this we know that the shear stress will be largest in the middle or the neutral axis Because that is where is the largest amount of the bending stresses being applied? Most difficult part of transverse shear stress is q or the first moment of area First Q is equal to the sum of y prime times the area prime the area prime is the area above or below the point you are examining for shear stress and The y prime value is the distance from the neutral axis to the centroid of the previously mentioned area You can use the full q value and subtract any holes from it and that will give you the needed Q value Now let’s try to calculate Q ourselves When we have a rectangle or a consistent shape like this q is very easy to calculate Because there is only one area and one y prime value to worry about we will look at what it’s like to take Q at the neutral axis in That case you only need to find the area above or below that point Looking above that point. We will get an area that looks like this and With it being a rectangle like this. We can just do base times height Next we will have to find the y prime which it will be the centroid of that rectangle that we just found Right in the Middle like this Then we could just multiply the two and get our prime times our area prime x or y prime Now let’s do a compound. Shape and a point that is not at the neutral axis We have to remember that whenever we try to find Q We need to take the sum of our areas multiplied by the centroids of each point That means that we need to calculate the area of both shapes above or below the point. I’ll do the area above When you’re looking at the centroids you just need to find the center of each of those areas and then you need to find their respective distances to the neutral axis Now we are going to do an example problem where we will find the maximum transfer of shear stress the equation of course is Vq i t and The inertia for this object is pretty familiar to calculate, so I will go ahead and do that for you Then the thickness is the thickness at the point that you are examining so we since we are examining the mat for the maximum which is at the neutral axis there will be thickness of 3 we already know what the shear force is and Now we’re left with Q which is the long part about transverse shear stress we will do what we have done before and we will break up the shape into two rectangles and Focus on the two shapes and calculate the first moment of areas for each shape and then we will add them together this is the result of that calculation and Then we just plug in the values for each of these Parts of the equation and we get nine hundred twenty four point six five eight PSI for our transfer shear stress (The correct answer for i is actually 1703.33 in ^4)

## 10 comments on “Transverse Shear Stress”

1. Tony Richmond Post author

Very helpful video, I'm finally starting to feel like I understand this now. Quick question: I got 1467 psi for the answer to that last question, whereas you got about 925 psi. I used all of the same values you did. Am I missing something?

2. Chance Reeves Post author

Wish you would have gone a little more into the Q calculation since as you even stated, that is the hardest part.