Why does shear flow include the full width, not just contact area?

[fonseh]

Homework Statement

For QB , why shouldn't the QB = red part only ?

Homework Equations

The Attempt at a Solution

Is there anything wrong with the solution given ?
Since When we 'cut ' the boards , the b is the red part which in contact with the other board , right ? [/B]

 

[PhanthomJay]

Homework Statement

For QB , why shouldn't the QB = red part only ?

Homework Equations

The Attempt at a Solution

Is there anything wrong with the solution given ?
Since When we 'cut ' the boards , the b is the red part which in contact with the other board , right ? [/B]

Nothing wrong with solution. Remember when determining bolt shear, use the full area of connected part when determining Q.

 

[Raeksis]

Sorry to bump this but when finding QB why can we not use one of the boards on the left or right? Why the center board?

 

[PhanthomJay]

Sorry to bump this but when finding QB why can we not use one of the boards on the left or right? Why the center board?

You can do it that way and get the same result without having to divide by 2 when you use the center board, because now there is just one shear plane instead of 2 when using the first method.

 

[Raeksis]

You can do it that way and get the same result without having to divide by 2 when you use the center board, because now there is just one shear plane instead of 2 when using the first method.

But I was thinking that only works here because the boards are the same dimensions.

In a question like this below (b), if I use one of the side boards I get a different (wrong) answer than if I use the center board.

 

[PhanthomJay]

But I was thinking that only works here because the boards are the same dimensions.

In a question like this below (b), if I use one of the side boards I get a different (wrong) answer than if I use the center board.

View attachment 196206

Part b is a bit more tricky than part a because in part b, the longitudinal shear flow across the nail is into the plane of the page (z direction) on the yz side face of a cubic element, in contrast to part a where the longitudinal shear flow across the nail is into the plane of the page (z direction) on the xz top face of a cubic element. Consequently, in part b, the shear flow is horizontally distributed across the top board, so you need to find Q based on the area of the board in between the nailed joints, and the vertical distance from its centroid to the neutral axis. Then divide result by 2 when determining shear flow, because there are 2 shear planes.
Alternatively, you could use the Q of the area outside of the top cuts, but when so doing, you must use the full area , that is, the area of both vertical pieces times the vertical distance of its centroid to the neutral axis. This a more tedious way of finding it.
Part b is a stronger connection than part a, because the Q in part b is less.