Shear flow along a triangular member

[into space]

Homework Statement

Homework Equations

qs1(0)=qs3(5)
qs2(0)=qs1(5)
qs3(0)=qs2(6)

Vy=0

q(s)=-Vy/Iyy*Q(s)

Where Q(s)=y*A
Where y=y coordinate of centroid and A=Area

The Attempt at a Solution

To be honest I'm not sure how to separate the q(0) term, nor do I know what the physical significance of q(0) is (it's the shear flow, but is it the total shear flow at point O?). I've tried setting up the problem like:
qs1(0)=q(0)=qs3(5)=q(0) so q(0)=q(0)
but that doesn't give me any information. I've also tried:
qs2(0)=-7.5*Vz*t/Iyy+q(0)
qs3(0)=-7.5*Vz*t/Iyy+q(0)

 

[SteamKing]

The shear flow q(s) is a function of the length coordinate s. Along each of the sides s1, s2, and s3, there is a point where s = 0. The location of the shear center suggests that the section is open at some point. If point O is the location where the section is open, what must the value of q(0) be?

 

[into space]

Thanks for the reply.

Hmm, I see what you are saying. So at s1=0, and the shear at point O is zero, then qs1(0)=-3*Vz*t*(0)^2/(10*Iyy)+q(0)=0 which means q(0) has to equal 0. Can you explain how you know there has to be an open section just from looking at the shear center?

 

[SteamKing]

The shear center is located outside of the triangular section. I believe most closed sections have the shear center located somewhere in their interiors. If the section is indeed open, then the shear flow starts with a zero value at the free end of the section. This fact is used when analyzing the shear flow in closed sections.

 

[nvn]

into space: The cross section is not open. You can see, from the given diagram, the cross section is closed.

In section 1 of post 1, why are you listing five values of q(0), a through e? When you state a question, you need to explain what is being listed. Why are you listing those q(0) values? Are you saying this is a multiple choice question? Is this an exam question?

q(s)=-Vy/Iyy*Q(s)

Wrong. Vy = 0.

Where Q(s)=y*A

Wrong. Vy = 0. Keep trying. By the way, excellent diagram. Nice work.

... nor do I know what the physical significance of q(0) is (it's the shear flow, but is it the total shear flow at point O?).

No, it is not. q(0) is just a constant. Your task is to determine the value of that constant.

 

[nvn]

into space: My first sentence in the last line of post 5 might be wrong. You might be right. q(0) might be the total shear flow at point O.