shear stress at particular point in beam

[johnson9883]

In the example , i suspect the selected A (area) is wrong... From the notes , A' is the area of top (or bottom ) portion of the member cross sectional area . But , in the example , we could see that the selected area is located to the right of the point where shear stress is calculated , is the notes wrong ?

 

 

IMO , the selected A' should look like this , right ? (refer to green part in the 3rd photo )

 

 

[Endy0816]

No, the notes are correct for horizontal shear stress.

[johnson9883]

No, the notes are correct for horizontal shear stress.

why ? I dont understand ... for the green part , my working is the length of horizontal I-beam x (19.6mm) (122.22mm - (19.6/2) ) ,

 

But , unfortunealy , the length of horizontal I-beam is not given .....

 

I dont understand the author's working in notes , can you explain further ?

[studiot]

Here is a quick sketch I hop will help explain.

 

The flange shear is the horizontal shear across the vertical dashed section through the point a in the sketch.

 

The formula your book gives is derived by balancing the moments forces at a, due to the hatched section of flange to the right of a and forces to the left of a du to the main loading.

 

Although the formula has almost the same form as the one in your other question, it is different in that the breadth of the beam is replaced by the thickness of the flange since the forces considered. are at right angles.

 

You need to understand shear in beams in terms of three dimensions, not 2.

 

[johnson9883]

Here is a quick sketch I hop will help explain.

 

The flange shear is the horizontal shear across the vertical dashed section through the point a in the sketch.

 

The formula your book gives is derived by balancing the moments forces at a, due to the hatched section of flange to the right of a and forces to the left of a du to the main loading.

 

Although the formula has almost the same form as the one in your other question, it is different in that the breadth of the beam is replaced by the thickness of the flange since the forces considered. are at right angles.

 

You need to understand shear in beams in terms of three dimensions, not 2.

 

hshear1.jpg

Do you mean that if the shear force is in this direction (green arrow to left and right ) , then my area of green part would be correct ?

 

So, the shear force in the previous diagram you posted is inside and outside of the book ?

Here is a quick sketch I hop will help explain.

 

The flange shear is the horizontal shear across the vertical dashed section through the point a in the sketch.

 

The formula your book gives is derived by balancing the moments forces at a, due to the hatched section of flange to the right of a and forces to the left of a du to the main loading.

 

Although the formula has almost the same form as the one in your other question, it is different in that the breadth of the beam is replaced by the thickness of the flange since the forces considered. are at right angles.

 

You need to understand shear in beams in terms of three dimensions, not 2.

 

hshear1.jpg

it's not stated in the question whether the shear force is applied in which direction , how do you know the direction of shear force which is insdie and outside of book ?

[Endy0816]

But , unfortunealy , the length of horizontal I-beam is not given .....

 

I dont understand the author's working in notes , can you explain further ?

 

It isn't needed(in this case).

 

Just need to know from wherever Point 'a' is at to the nearest edge.

[johnson9883]

 

It isn't needed(in this case).

 

Just need to know from wherever Point 'a' is at to the nearest edge.

why ? is it due to the case that the studiot post earlier ? the shear force act inside and outside of book on the beam ?

[studiot]

 

Do you mean that if the shear force is in this direction (green arrow to left and right ) , then my area of green part would be correct ?

So, the shear force in the previous diagram you posted is inside and outside of the book ?

 

 

I also said you need think in 3 dimensions.

 

Did your book derive the formulae for you?

 

Yes the shear is along the beam as I showed, here is a better diagram, have you heard of complementary stresses?

 

 

 

[johnson9883]

No , what is com

 

 

 

I also said you need think in 3 dimensions.

 

Did your book derive the formulae for you?

 

Yes the shear is along the beam as I showed, here is a better diagram, have you heard of complementary stresses?

 

hshear2.jpg

 

No , what is complemetary stress ?

 

 

I also said you need think in 3 dimensions.

 

Did your book derive the formulae for you?

 

Yes the shear is along the beam as I showed, here is a better diagram, have you heard of complementary stresses?

 

hshear2.jpg

 

 

In the notes , why the I-beam is sheared in the direction outward and inward of the book ? it's not stated in the notes earlier in example , right ?

Edited November 6, 2016 by johnson9883

[studiot]

 

 

In the notes , why the I-beam is sheared in the direction outward and inward of the book ? it's not stated in the notes earlier in example , right ?

 

Think about how the I beam is loaded.

You are only considering loading to be applied on the central axis.

In fact great effort is made in design and construction to make sure this is so.

 

So think about how is any stress transferred to the flanges?

 

This is explained in the bottom paragraph on the left hand page I posted in post#8, and drawn in the diagram on the right hand page.

 

I will explain further about complementary stresses, but briefly they are stresses that are induced in planes at right angles to the primary stress or load to maintain static equilibrium, both force and moment.

 

Have you revisited your original post about beam stresses?

 

http://www.scienceforums.net/topic/100399-shear-stress-at-boundary-of-beam/