Shear flow in thin wall members

[fonseh]

Homework Statement

In the notes , I don't understand that flange is thin , and the top and bottom surface are free of stress , can someone help to explain please?

Secondly , why the q' is assumed to be q ' throughout the flange is assumed to be 0 ? why are they stress free ? We could see that , the shear force V is applied to the top of the beam right ?

Homework Equations

The Attempt at a Solution

why are they stress free ? We could see that , the shear force V is applied to the top of the beam right ... So , there must be some magnitude of stress acting on top or bottom or the beam [/B]

 

[PhanthomJay]

Homework Statement

In the notes , I don't understand that flange is thin , and the top and bottom surface are free of stress , can someone help to explain please?

Secondly , why the q' is assumed to be q ' throughout the flange is assumed to be 0 ? why are they stress free ? We could see that , the shear force V is applied to the top of the beam right ?

Homework Equations

The Attempt at a Solution

why are they stress free ? We could see that , the shear force V is applied to the top of the beam right ... So , there must be some magnitude of stress acting on top or bottom or the beam [/B]

that is right. The transverse Horizontal shear stresses ( and accompanying longitudinal shear stress) are non zero on the flange except at the ends. The reference to zero shear stress in the flange is talking about negligible vertical shear stress in the flange due to assumed thin wall.

 

[fonseh]

The reference to zero shear stress in the flange is talking about negligible vertical shear stress in the flange due to assumed thin wall.

why the wall is thin , and the shear stress is negligible ? ?

 

[fonseh]

that is right. The transverse Horizontal shear stresses ( and accompanying longitudinal shear stress) are non zero on the flange except at the ends. The reference to zero shear stress in the flange is talking about negligible vertical shear stress in the flange due to assumed thin wall.

do you mean likt his ? in the notes , it's stated that the shear flow components that acts parallel ro the sides of flange will be considered ?

Does it mean that the red shear flow will be considered ( since it's side of flange) ? while the blue shear flow will be ignored since it's top and bottom are free of stress ?

 

[PhanthomJay]

The plot thickens. The blue (horizontal shear flow) and the red (longitudinal shear flow) exist simultaneously. You can't have one without the other. What is ignored is the small vertical shear stress in the flange, assumed to be zero since the web carries almost all the vertical shear. Also, you have an extra red arrow in there pointing in the wrong direction.

 

[fonseh]

since the web carries almost all the vertical shear.

why the web carries almost all the vertical shear ? how to know it ? do you mean shear flow ? the web carries almost all the vertical shear ? (refer to the photos uploaded , do you mean it is the vertical arrow alll pointing downwards in the web ? while no vertical arrow at all in the flange , so the web is assumed to be taking all the vertical shear ?

 

[PhanthomJay]

No upload. But web carries most of vert shear, flanges only a small amount

 

[fonseh]

No upload. But web carries most of vert shear, flanges only a small amount

sorry , image here

 

[PhanthomJay]

sorry , image here

This is getting way too confusing. Image shows vert shear stress distribution in web, and horiz shear stress distribution in flange. Vert shear stress distribution in flange (the 3 MPa vert shear stress we talked about earlier) not shown.

 

[fonseh]

No upload. But web carries most of vert shear, flanges only a small amount

can you explain on why But web carries most of vert shear, flanges only a small amount ?

 

[PhanthomJay]

can you explain on why But web carries most of vert shear, flanges only a small amount ?

Recall that vert shear stress is VQ/it. For flange, t is quite large , it is the full width of the flange, so when you divide by a large number you get a small number relative to the web shear stress where t is only the web thickness.

 

[fonseh]

Recall that vert shear stress is VQ/it. For flange, t is quite large , it is the full width of the flange, so when you divide by a large number you get a small number relative to the web shear stress where t is only the web thickness.

Can i use your theory to explain the horizontal shear stress ?
to find horizontal shear stress , we have to cut vertically , since the 'thicnkness' at the web is large , so the horizontal shear stress is so small compared to the horizontal shear stress at web , so , horizontal shear stress at web is negligible ?

 

[PhanthomJay]

Can i use your theory to explain the horizontal shear stress ?
to find horizontal shear stress , we have to cut vertically , since the 'thicnkness' at the web is large , so the horizontal shear stress is so small compared to the horizontal shear stress at web , so , horizontal shear stress at web is negligible ?

I am not following you. Horizontal shear stress is in the flange at a vert cut through the flange. Flange thickness is small. Regarding web, that is just vertical shear stress, which controls design..

 

[fonseh]

I am not following you. Horizontal shear stress is in the flange at a vert cut through the flange. Flange thickness is small. Regarding web, that is just vertical shear stress, which controls design..

is my theory of

to find horizontal shear stress , we have to cut vertically , since the 'thicnkness' at the web is large , so the horizontal shear stress is so small compared to the horizontal shear stress at web , so , horizontal shear stress at web is negligible ? only the horizontal shear stress at the flange is considered ?

wrong ?

 

[PhanthomJay]

is my theory of

to find horizontal shear stress , we have to cut vertically , since the 'thicnkness' at the web is large , so the horizontal shear stress is so small compared to the horizontal shear stress at web , so , horizontal shear stress at web is negligible ? only the horizontal shear stress at the flange is considered ?

wrong ?

For an I beam, in order to find the longitudinal shear stress in the flange at a vertical cut thru the flange, you use the area to the right of the cut in calculating Q, and then the longitudinal shear stress acts into the plane ( along the beam ) parallel to the face of the cut, and along the side of the cut. In order to find the longitudinal shear stress in the web at a horizontal cut thru the web, you use the area above the cut in calculating Q, and then the longitudinal shear stress acts into the plane ( along the beam ) parallel to the face of the cut, and along the top of the cut.

In looking at a vertical flange cut near the web, the shear stress is about 1/2 the shear stress of a horizontal web cut near the flange, because the Q area for the former is about half the Q area of the latter. Neither stress is very significant unless you have a built-up beam requiring nails or welds in which case the concept of shear flow determines weld size or nail spacing.

 

[fonseh]

In looking at a vertical flange cut near the web, the shear stress is about 1/2 the shear stress of a horizontal web cut near the flange, because the Q area for the former is about half the Q area of the latter.

do you mean apply the cut at the center of the web ?

just like the case below ?

if so , then i found that the Q fir the vertical cut and horizontal cut are the same ... taking the diagram below as example , i have skteched the Q for vertical cut and horizontal cut ...
so , the Q for the vertical cut is 30*50*15 =22500 ,, Q for the horizontal cut = 30*50*25 =37500 , so . it;s clear that the Q for the horizontal cut is higher , so the vertical shear stress is higher , $$\tau = VQ/It $$ , so the vertical shear stress at the web is higher , so it's considered , while the horizontal shear stress us lower at the web , so , it's ignored ?

 

[PhanthomJay]

I don't know what these numbers are that you are using.

There are generally 3 directions of shear stress in a member...vertically up and down along the cross section, horizontally left to right or right to left along the cross section, and longitudinally into and out of the plane of the cross section.

In the web, shear stresses are vertical and longitudinal. The stresses are determined by cutting horizontally at the point of interest, and using the Q value of the area above the cut, and then the longitudinal stresses act at the top and bottom of the cut face, into the plane. There are no horizontal shear stresses in the web , since if you were to make a vertical cut thru the entire web, the Q to the right of the cut would be zero, since the centroid of the area to the right of the cut is at the neutral axis, such that the vert distance from the centroid to the NA is 0.

In the flange, shear stresses are vertical, horizontal, and longitudinal. The horizontal stresses are determined by cutting vertically at the point of interest, and using the Q value of the area to the right of the cut, and then the longitudinal stresses act at the side of the cut face, into the plane. There are small average vertical shear stresses in the web , which are typically ignored except when designing welds for a cover plate over the flange. The assumed zero vertical shear stress in the web, and its associated longitudinal stress , designated as (q'), is shown in figure e of the 1st post. The horiz shear stress , q, is non-zero.

 

[fonseh]

since the centroid of the area to the right of the cut is at the neutral axis, such that the vert distance from the centroid to the NA is 0.

why ? can you explain it with diagram ?
do you mean cut the web vertically thru the center of the web ?

 

[fonseh]

I don't know what these numbers are that you are using.

There are generally 3 directions of shear stress in a member...vertically up and down along the cross section, horizontally left to right or right to left along the cross section, and longitudinally into and out of the plane of the cross section.

In the web, shear stresses are vertical and longitudinal. The stresses are determined by cutting horizontally at the point of interest, and using the Q value of the area above the cut, and then the longitudinal stresses act at the top and bottom of the cut face, into the plane. There are no horizontal shear stresses in the web , since if you were to make a vertical cut thru the entire web, the Q to the right of the cut would be zero, since the centroid of the area to the right of the cut is at the neutral axis, such that the vert distance from the centroid to the NA is 0.

In the flange, shear stresses are vertical, horizontal, and longitudinal. The horizontal stresses are determined by cutting vertically at the point of interest, and using the Q value of the area to the right of the cut, and then the longitudinal stresses act at the side of the cut face, into the plane. There are small average vertical shear stresses in the web , which are typically ignored except when designing welds for a cover plate over the flange. The assumed zero vertical shear stress in the web, and its associated longitudinal stress , designated as (q'), is shown in figure e of the 1st post. The horiz shear stress , q, is non-zero.

the diagram represent the web , if i apply a vetical cut thru the center of the web , the centroid of the area is the red dot , so , the y in Q = Ay is measured from the center to the centroid of the yellow area , why you said that y = 0 ? I'm confused

 

[PhanthomJay]

If you apply a vertical cut thru the web, the area to the right of the cut is the blue area. Its centroid is at the NA. The vertical distance from the centroid to the NA is 0.

 

[fonseh]

If you apply a vertical cut thru the web, the area to the right of the cut is the blue area. Its centroid is at the NA. The vertical distance from the centroid to the NA is 0.

ok , for flange , when we apply a vertical cut , the area is the area to the right of the cut , then , the vertical distance from the centroid to the NA is 0. so , horizontal shear stress in flange also = 0 ?

 

[fonseh]

I'm confused about the location of neutral axis now ...
No matter vertical or horizontal cut , the neutral axis is always horizontal ?

 

[fonseh]

There are no horizontal shear stresses in the web , since if you were to make a vertical cut thru the entire web, the Q to the right of the cut would be zero, since the centroid of the area to the right of the cut is at the neutral axis, such that the vert distance from the centroid to the NA is 0.

looking at a vertical flange cut near the web, the shear stress is about 1/2 the shear stress of a horizontal web cut near the flange, because the Q area for the former is about half the Q area of the latter

I'm confused now . in post 14 , you said that the shear stress is about 1/2 the shear stress of a horizontal web cut near the flange , but in post 16 , you said that the centroid of the area to the right of the cut is at the neutral axis, such that the vert distance from the centroid to the NA is 0.

 

[PhanthomJay]

ok , for flange , when we apply a vertical cut , the area is the area to the right of the cut , then , the vertical distance from the centroid to the NA is 0. so , horizontal shear stress in flange also = 0 ?

The vertical distance from the centroid of top flange area to the right of the cut , to the NA, is not zero. It's about 1/2 the depth of the beam.

 

[PhanthomJay]

[

I'm confused about the location of neutral axis now ...
No matter vertical or horizontal cut , the neutral axis is always horizontal ?

When applied beam loads are in the vertical direction, the NA is horizontal no matter of the cut location

I'm confused now . in post 14 , you said that the shear stress is about 1/2 the shear stress of a horizontal web cut near the flange , but in post 16 , you said that the centroid of the area to the right of the cut is at the neutral axis, such that the vert distance from the centroid to the NA is 0.

Post 14 is vert web shear stress close to the top flange. Post 16 is horiz web shear stress at NA. No part of the web, top , mid, or bot, has horiz shear stress. Attached shows horiz shear flow in flange

 

[fonseh]

In looking at a vertical flange cut near the web, the shear stress is about 1/2 the shear stress of a horizontal web cut near the flange, because the Q area for the former is about half the Q area of the latter.

Can you explain it further with diagram ? i don't understand . Why Q area for the former is about half the Q area of the latter ?

Since you said that Q area for the former is about half the Q area of the latter., so for a vertical flange cut near the web, the horizontal shear stress is about 1/2 the shear stress of a horizontal web cut near the flange... Is it true ?

 

[PhanthomJay]

Can you explain it further with diagram ? i don't understand . Why Q area for the former is about half the Q area of the latter ?

Since you said that Q area for the former is about half the Q area of the latter., so for a vertical flange cut near the web, the horizontal shear stress is about 1/2 the shear stress of a horizontal web cut near the flange... Is it true ?

Yes, about a half, , since the area to the right of a vert cut in the flange is about 1/2 the area above a horiz cut in the web, and the ybar of each area is the same.. I'll try to sketch something tomorrow.

 

[fonseh]

Yes, about a half, , since the area to the right of a vert cut in the flange is about 1/2 the area above a horiz cut in the web, and the ybar of each area is the same.. I'll try to sketch something tomorrow.

Sorry, , i mean Since you said that Q area for the former is about half the Q area of the latter., so for a vertical flange cut near the web, the horizontalshear stress is about double the shear stress of a horizontal web cut near the flange... Is it true ?

 

[PhanthomJay]

 

[fonseh]

View attachment 109259

ok , understand it...nw , i understand that why there's no horizontal shear stress in web .

But , i still don't understand why there's no vertical shear stress in flange , can you explain about it ?

 

[PhanthomJay]

ok , understand it...nw , i understand that why there's no horizontal shear stress in web .

But , i still don't understand why there's no vertical shear stress in flange , can you explain about it ?

there is a small vertical shear stress in the flange, but if you do the math using the same area above cut b, you get the same Q, but the flange thickness is 200, not 20, so the vertical shear stress is only about 10 percent on average
of the vertical shear stress in the web at b, or perhaps just 5 percent of the max vert shear stress at the NA, and further,much of that vert flange shear stress is fictitious because there is no shear stress at the free edges of the flange, vert shear is internal within the flange. Vert shear in flange is only useful when you want to strengthen the beam by welding a plate to the top flange, and the welds required are quite small because the vert shear stress is so small.

 

[fonseh]

same Q,

removed

 

[fonseh]

there is a small vertical shear stress in the flange, but if you do the math using the same area above cut b, you get the same Q, but the flange thickness is 200, not 20, so the vertical shear stress is only about 10 percent on average
of the vertical shear stress in the web at b, or perhaps just 5 percent of the max vert shear stress at the NA, and further,much of that vert flange shear stress is fictitious because there is no shear stress at the free edges of the flange, vert shear is internal within the flange. Vert shear in flange is only useful when you want to strengthen the beam by welding a plate to the top flange, and the welds required are quite small because the vert shear stress is so small.

ok , i don't understand why when we cut the portion of the flange or web , there are only 2 shear stress acting ? shouldn't be 3 stress ? for example , in the vertical cut at flange , the stress only act to the 2 faces of the beam flange only ? How about the top part ? why there's no stress over there ?

 

[PhanthomJay]

ok , i don't understand why when we cut the portion of the flange or web , there are only 2 shear stress acting ? shouldn't be 3 stress ? for example , in the vertical cut at flange , the stress only act to the 2 faces of the beam flange only ? How about the top part ? why there's no stress over there ?

in the flange cube, I didn't show the small vert shear stress which exists downward on the left face, and with its accompanying longitudinal stress which lies on the green area. In the web cube, there is no horiz shear stress, so that face has no stress shown. Note that in both cases there are equal and opposite shear stresses on the far faces of the cube, not shown for clarity.

 

[fonseh]

Note that in both cases there are equal and opposite shear stresses on the far faces of the cube, not shown for clarity.

far faces of the cube means the face behind ?