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Longitudinal shear
- Thread starter oranda
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Do you mean horizontal shear?TO imagine physically, consider a rectangular sectionn baeam of depth say 1 unit.Let the beam be divided into 4 layers of 1/4 unit each.Moment of inertia of the beam being proportional to d3 is 4*(1/4)3((cube))=4*1/64=1/16.
Now consider the beam withpot any layers moment of inertia of the beam proportional to 1(cube)=1
For the beam to act as a single unit therefore should be enough adhesion throughout the depth.Without this you are essentially reducing the moment of inertia of the beam by 16 times(thumbsdown)This is just to visualize physically horizontal shear.YOu can refer to strength of material books to get theoretical derivations(complimentary shear)
Now consider the beam withpot any layers moment of inertia of the beam proportional to 1(cube)=1
For the beam to act as a single unit therefore should be enough adhesion throughout the depth.Without this you are essentially reducing the moment of inertia of the beam by 16 times(thumbsdown)This is just to visualize physically horizontal shear.YOu can refer to strength of material books to get theoretical derivations(complimentary shear)
I use the following example to explain horizontal shear, which is an important design limit in wood design:
Take a deck of cards, hold it between thomb and middle finger, then push down on the center of the deck with your index finger. As the deck bends, you can see the cards sliding over one another. That's horizontal shear.
Max stress is Fvmax= 3V/2bd for a rectangular section
Take a deck of cards, hold it between thomb and middle finger, then push down on the center of the deck with your index finger. As the deck bends, you can see the cards sliding over one another. That's horizontal shear.
Max stress is Fvmax= 3V/2bd for a rectangular section
Guest
In case of the beam with layers each layer is free to slide with respect to others and acts as a shallow rectangular beam by itself.The sliding of the various layers show the tendency of the layers to shear along horizontal planes.The sliding is prevented by horizontal shear stresses.
Take two independent structural member stack one ontop of the other. If there is no horizontal shear between the two member, then they act independent. If horizontal shear stresses act at the interface of the two members, then this system will behave in a composite manner. Concrete by its nature is a composite material. It relies on the shear stress (bonding) between the binder material, aggregates & reinf. to carry loads.
From strenght of material, the shear stress between the contact surfaces is v=VQ/Ib where v is the horizontal shear stress, V is the shear force acting on the section in question, Q is the first moment of area of the member about the centroidal, I is the uncrack moment of inertia and b is the width.
Hope this help.
From strenght of material, the shear stress between the contact surfaces is v=VQ/Ib where v is the horizontal shear stress, V is the shear force acting on the section in question, Q is the first moment of area of the member about the centroidal, I is the uncrack moment of inertia and b is the width.
Hope this help.
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