Calculating Shear Stress on a Rivet in Tension with Angle of Load

[Stacyg]

A load of 5kN is applied to the tensile member shown in the figure below and is carried at the joint by a single rivet of 20mm diameter. The angle of the joint is 60 degrees to the axis of the load (the axis of the rivet is at 30 degrees to the line of action of the load P). Calculate:
(a) the tensile shear stress in the rivet
(b) shear stress in the rivet

The figure is attached. I know how to calculate the stress but I'm not sure how to calculate it on an angle like this. I'm guessing you use the same equation and maybe times it by 5sin60 or do i use 30.

Thanks Stacy

 

[nvn]

For shear stress, one of the answers you listed is correct. You just need to use trigonometry to determine which one is correct.

 

[Mene]

Hello Stacy,

Thank you for your question. I would be happy to provide you with a response.

To calculate the shear stress on a rivet in tension with an angle of load, we can use the formula:

Shear stress = Load / Area

(a) To calculate the tensile shear stress in the rivet, we first need to find the area of the rivet. This can be done by using the formula:

Area = π * (diameter/2)^2

In this case, the diameter of the rivet is 20mm, so the area would be:

Area = π * (20/2)^2 = 314.16 mm^2

Next, we need to find the component of the load that is acting in the direction of the rivet. This can be done by using the formula:

Load component = Load * sin(angle)

In this case, the angle is 60 degrees, so the load component would be:

Load component = 5kN * sin(60) = 4.33 kN

Now, we can plug these values into the formula for shear stress:

Shear stress = 4.33 kN / 314.16 mm^2 = 0.0138 MPa

Therefore, the tensile shear stress in the rivet is 0.0138 MPa.

(b) To calculate the shear stress in the rivet, we can use the same formula:

Shear stress = Load / Area

However, this time we will use the entire load of 5kN, since we are calculating the total shear stress on the rivet. So the equation would be:

Shear stress = 5 kN / 314.16 mm^2 = 0.0159 MPa

Therefore, the total shear stress on the rivet is 0.0159 MPa.

I hope this helps to answer your question. Please let me know if you need any further clarification. Keep up the great work in your studies!