Shear stress at different points

[fonseh]

Homework Statement

In this notes , i don't understand how the Q=(Ay) of the is considered ...

Homework Equations

The Attempt at a Solution

I think the both Q at part C and part B should be = (60)(15)(mm^2) ... i have redrawn the structure , i am not sure whether it is correct or not...
From the definition of shear flow , A is the cross section area of segment that is connected to the beam at juncture where the shear flow is calculated . [/B]

 

[PhanthomJay]

You changed dimensions from inches to mm incorrectly, but anyway, book solution looks good. At B you find the vert shear stress and complimentary longitudinal shear stress is into the page and they the plane of the nail so you use the full area above b for calculating Q then divide by 2 since there are 2 webs.

 

[fonseh]

You changed dimensions from inches to mm incorrectly, but anyway, book solution looks good. At B you find the vert shear stress and complimentary longitudinal shear stress is into the page and they the plane of the nail so you use the full area above b for calculating Q then divide by 2 since there are 2 webs.

ok , why in the author's working , the red area is included ? I think the red area is not included because the horizontal nail is acting at C , so , according to the formula , the A ' is the area is the area that is connceted to the beam at the juncture , so , i think that the red part is not included

 

[PhanthomJay]

ok , why in the author's working , the red area is included ? I think the red area is not included because the horizontal nail is acting at C , so , according to the formula , the A ' is the area is the area that is connceted to the beam at the juncture , so , i think that the red part is not included

I understand your reasoning, but it is incorrect. Suppose the beam was a solid hollow box, no nails whatsoever, and you wanted to determine the shear stress in the web at b. You would use the full area of the upper flange (7.5 inch width) in calculating Q, and in calculating t, that would be twice the web thickness because there are 2 webs. The entire flange tends to try to slip longitudinally off the webs. It makes no difference to the beam whether it is nailed vertically or horizontally or not at all, as long as there is no slippage, either the nails or the solid wood without nails takes the shear.

It's a bit different at C, because now the upper middle flange tends to slip longitudinally off the webs, so you use hat 4.5 inch width in the Q calcs. Note that the horizontal nails do 't have to be spaced as close as the vert nails, because they carry less stress.