Mechanics of materials - shear flow in built up members

[nate_cal]

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.

 

[FEAnalyst]

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.

 

[Lnewqban]

Welcome!

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