Mechanics of materials - shear flow in built up members

In summary, The conversation is about the shear formula and understanding the use of A' in the calculation. The speaker is confused about why only one of the top boards is used for A' in the calculation instead of both, when the bolt goes through all three boards. The expert explains that in this case, analyzing one section is sufficient since the beam is symmetrical and the shear flow is evenly distributed. The expert also provides additional resources for further understanding.
  • #1
nate_cal
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TL;DR Summary
I do not really understand how to determine the value Q from the shear formula for this example.
Hello!

I am new to mechanics of materials and I am very confused about the problem below. So the shear formula is:

tau = VQ/It

From the book (Hibbeler) I understand that Q is "y'A', where A' is the cross-sectional area of the segment that is connected to the beam at the juncture where the shear flow is calculated, and y' is the distance from the neutral axis to the centroid of A'". However, for this case I do not understand why A' is only one of the top boards (red area) and not both, if the bolt goes through all the 3 boards.

question.PNG
 
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  • #2
This example is from the chapter about built-up members - beams consisting of several connected parts. Each segment is treated separately in these calculations and thus the cross-sectional area of a single segment is used.
 
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  • #3
Welcome! :cool:

Could you show us the solution or explanation provided by the book?
It seems the goal is to determine the minimum resistance to shear force of each of the sections of one bolt under that type of load.

Why A' is only one of the top boards?
Since the beam is symmetrical and both cross-sections of one bolt have similar area, analyzing one is sufficient, as the shear flow is evenly distributed for both cross-sections, as well as for both, top and single bottom wood boards.

Yours is case b) in the picture below.

Please, see:
http://www.engineeringcorecourses.com/solidmechanics2/C3-transverse-shear/C3.1-shear-flow/question2/

https://mathalino.com/reviewer/mechanics-and-strength-of-materials/shear-stress

Shear flow.jpg


 
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1. What is shear flow in built up members?

Shear flow in built up members refers to the distribution of shear stress along the cross-section of a structural member that is composed of multiple individual parts, such as beams or columns. It is an important concept in mechanics of materials as it affects the strength and stability of a structure.

2. How is shear flow calculated?

Shear flow is calculated by dividing the shear force acting on a member by the moment of inertia of the cross-section. This gives the shear stress, which can then be multiplied by the distance from the neutral axis to determine the shear flow at a specific point.

3. What factors affect shear flow in built up members?

There are several factors that can affect shear flow in built up members, including the shape and dimensions of the individual parts, the material properties, and the type and magnitude of the applied load. Additionally, the method of connection between the individual parts can also impact the shear flow.

4. How does shear flow impact the design of built up members?

Shear flow is an important consideration in the design of built up members as it can affect the overall strength and stability of the structure. Engineers must carefully calculate and distribute the shear flow to ensure that the individual parts of the member can withstand the applied loads and maintain structural integrity.

5. Can shear flow be controlled in built up members?

Yes, shear flow can be controlled in built up members through various design techniques. These include changing the dimensions or shape of the individual parts, altering the method of connection between the parts, and using reinforcement or stiffeners to redistribute the shear flow. Computer simulations and testing can also be used to optimize the design and control the shear flow in built up members.

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