# The Shear-Center Concept

**Also see Shear Center with Examples**

What happens when loads act in a plane that is not a plane of symmetry?

-Loads must be applied at particular point in the cross section, called shear center, if the beam is to bend without twisting.

**Shear Stress distribution **

- Constrained by the shape of the cross section

- Its resultant acts at the shear center

- Not necessarily the centroid

**Shear Center**

- A lateral load acting on a beam will produce bending without twisting only if it acts through the shear center
- The shear center

- Is a property of the cross section like the centroid
- It lies on an axis of symmetry

- For a doubly symmetric section S and C coincide

**Why a property of the cross section? **

**Locating Shear Centre**

**Unsymmetric**** Loading of Thin-Walled Members**

- Beam loaded in a vertical plane of symmetry deforms in the symmetry plane without twisting.

- Beam without a vertical plane of symmetry bends and twists under loading.

**Unsymmetric**** Loading of Thin-Walled Members**

- If the shear load is applied such that the beam does not twist, then the shear stress distribution satisfies

*F*and*F’*indicate a couple*Fh*and the need for the application of a torque as well as the shear load.

- When the force P is applied at a distance
to the left of the web centerline, the member bends in a vertical plane without twisting.*e*

**Shear stress distribution strategy **

- Determine location of centroid and
*I*_{yy}*,**I*and_{zz}*I*as needed – (symmetric sections subject to_{yz}*V*needs only_{y}*I*)_{zz}

- Divide section into elements according to geometry (change in slope)
- Start with a vector
*s*following element center line from a free end - Calculate first moment of area(s). This determines the shear flow distribution

– Negative shear value indicate direction of shear flow opposite to assumed vector *s*

- Calculate first moment of area(s). This determines the shear flow distribution
- For symmetric sections subject to bending about one axis
- Elements parallel to bending axis–Linear distribution
- Elements normal to bending axis–Parabolic distribution
- For unsymmetric sections shear flow in all elements is parabolic

- When moving from one element to another the end value of shear in one element equals the initial value for the subsequent element (from equilibrium)

**Shear Centres for Some Other Sections**

**Shear Center **

- How to locate Shear Center?

- Doubly symmetric cross sections– Coincides with centroid
- Singly symmetric cross sections– Lies on the axis of symmetry

- Thin-walled open sections

- Opposite side of open part

**Doubly or singly symmetric section**

**Also see Shear Center with Examples**

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Thankfulness

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How can I copy these nice documentation into my data base? Thank you very much for your time.

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thank u sir.

Thanks for your assistance.

Can anybody tell me what is the application? where it is critical to calculate shear center?

It is useful to nullify the twisting moment in the element due to torsion.