Find an expression for the shear stress of this figure

In summary, the speaker is trying to define the y distance in their coordinate system and needs to find an expression for the shear stress on a figure. They have made a cut and defined the length from the start of the figure to the cut as z1. The formula for calculating the shear stress is given, but the speaker is having trouble with the area A of the figure, which is expressed as t*(400-z1). They are also unsure of the y distance and believe their calculation may be incorrect. They request someone to explain how the y distance should be expressed.
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Summary: I have trouble to define the y distance in my coordinatesystem

1565209715764.png


I need to find an expression for the shear stress on the I figure, where the green parabola illustrates the function. I made a cut, where I defined the length from the start of figure I to the cut as z1. The formula for calculating the shear stress:
τ=V*Q/I*t
V=183 kN (Shear)
Q=A*y
I=804.95*10^6 mm^4 (inertiamoment)
t=20 mm (thickness)

Ignore the II figure. My problem is on Q=A*y

The area A of the figure on my analyze is:
A=t*(400-z1)

The y distance confuses me and from the assignment, the center of the gravity is `y=368.44 mm. So my thought is that the distance from the center of the figure I and the `y=368.44 mm is expressed:
y=(400mm/2 - z1 - 368.44 mm)

So my function of shear stress is:

τ=183*10^3N* (t*(400-z1)) * (400mm/2 - z1 - 368.44 mm) / I * t

I think my y distance is wrong so would appreciate if someone could explain me how it is suppose to be.
 
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  • #2
I’m not sure of your signage, but the math error is that you forgot to divide z1 by 2 in your expression for y. Also the parabolic green curve is not correctly shown.
 
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What is shear stress?

Shear stress is the force per unit area that acts parallel to the surface of an object, causing it to deform or slide.

How is shear stress calculated?

Shear stress is calculated by dividing the applied force by the cross-sectional area of the object perpendicular to the direction of the force.

What is the significance of finding an expression for shear stress?

Finding an expression for shear stress allows us to accurately predict and analyze the behavior of materials under different types and magnitudes of forces.

What factors affect the shear stress of an object?

The shear stress of an object is affected by the magnitude of the applied force, the cross-sectional area of the object, and the material properties of the object, such as its elasticity and viscosity.

How can we use the expression for shear stress to design and engineer structures?

By understanding the shear stress on different materials and structures, we can design and engineer them to withstand various types and magnitudes of forces, ensuring their structural integrity and safety.

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