# Calculating shear stress in a beam?

• shannonxtreme
In summary, the equation for shear stress is VQ/It, where V is the shear force, Q is the first moment of area, I is the moment of inertia, and t is the thickness of the material at the point of interest. There is no general formula for Q, as it depends on the specific cross section being analyzed. The formulas VQ/I t and F(A*y-bar)/I t are equivalent, with Q representing the first moment of area from the point of interest to the outermost edge of the section. For more specific calculations, reference a book on strength of materials or provide further details for a discussion.
shannonxtreme
The equation for shear stress as I know it is VQ/It where V is the shear force, Q is the first moment of area(?), I is moment of inertia and t is the length of the section in question.
My question is, is there a general formula for Q? In my Solid Mechanics notes I've written that Q = ∫y.dA but for some reason this isn't giving me the answers I get from the equation τ= F. (A.ybar/I.t)
Could someone write down the general formula for Q?

shannonxtreme said:
The equation for shear stress as I know it is VQ/It where V is the shear force, Q is the first moment of area(?), I is moment of inertia and t is the length of the section in question.
My question is, is there a general formula for Q? In my Solid Mechanics notes I've written that Q = ∫y.dA but for some reason this isn't giving me the answers I get from the equation τ= F. (A.ybar/I.t)
Could someone write down the general formula for Q?
There is no general formula for Q. Q represents the first moment of area of the cross section from the point at which you wish to calculate the shear stress to the outermost edge of the section. Q does have to be calculated with reference to the centroid of the section, however.

The quantity t represents the thickness, not the length of the material in way of the shear stress location.

As to your formulas for calculation, VQ / I t is just a re-statement of F (A*y-bar) / I t, where the quantity A*y-bar = Q and F = V. In my experience, VQ / I t seems to be preferred in the US, whereas the other formula was used quite a lot in older texts written in the UK.

A book on strength of materials should illustrate how to treat the calculation of Q for specific examples of different cross sections.

If you have a particular case where you need to analyze the shear stress, please feel free to post this information and we'll be glad to discuss it with you.

## 1. What is shear stress in a beam?

Shear stress in a beam is the internal force that is created when a beam is subjected to external forces that cause it to bend or deform. It is a result of the shear force acting on the cross-sectional area of the beam.

## 2. How is shear stress calculated in a beam?

Shear stress in a beam can be calculated by dividing the maximum shear force acting on the beam by the cross-sectional area of the beam. The formula for shear stress is τ = V/A, where τ is the shear stress, V is the shear force, and A is the cross-sectional area.

## 3. What units are used to measure shear stress in a beam?

Shear stress in a beam is typically measured in units of force per unit area, such as pounds per square inch (psi) or newtons per square meter (N/m²).

## 4. What factors affect shear stress in a beam?

The amount of shear stress in a beam is affected by the magnitude of the applied force, the geometry of the beam, and the material properties of the beam, such as its modulus of elasticity and shear modulus.

## 5. Why is calculating shear stress important in engineering?

Calculating shear stress in a beam is important in engineering because it helps engineers determine the structural integrity of a beam and ensure that it will not fail under the expected loads and forces. This information is crucial in the design and construction of safe and reliable structures.

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