What are methods to calculate shear center?
6 Answers
Note:- I am not an expert. I am student of Structural Engineering. So my answer may have error or mistake.
Shear Center is a point through which if the external load passes, then there will not be any twisting of the section. In other words, section will only be subjected to bending. It won't be subjected to Torsion.
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( Torsion due to Load being applied at a distance eccentric to the shear center)
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(No Torsion, Only Bending due to load being applied at the shear center)
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( Torsion due to Load being applied at a distance eccentric to the shear center)
In general, Shear center lies on the axis of symmetry. So for doubly symmetric section shear center lies at the intersection of the two axes of symmetry. Thus for doubly symmetric sections, shear center coincides with the centroid. If the section has only one axis of symmetry then shear center will lie on that axis at distance eccentric to the non-symmetric axis.
In order to determine the position of shear center, the direction of shear flow in a section needs to be known. For most of the regular sections the shear flow is smooth and logical. In other words, the direction of shear flow doesn't get changed abruptly. There are examples where the direction of shear flow changes abruptly.
Some important points :-
1) Shear is taken up by the elements which are parallel to the direction of applied shear.
2)The direction of shear flow in the elements parallel to the applied shear is always in opposite direction to that of applied shear.
3) For a shear acting in the direction parallel to the axis of symmetry, there will be point/s where shear flow will either converge or diverge. Such points can either be called as source or sink. Such points are located at the intersection of the axis of symmetry (passing through the centroid) with the section.
4)The value of shear flow is zero at the points where cross section is open to air.
In the following image below, shear flow is shown in various sections.
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In the figure 1(a), points C & D represent source/sink (point where shear flow is zero). Note that external shear V is shown to be acting at shear center. The total resisting shear force in the element/s parallel to the applied shear is equal to V (applied shear). For example in figure 2(b) shear force taken up by each flange (BA & CD) is equal to V/2.
The corresponding shear flow diagram or Q(1st moment of area) diagram is attached below.
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The shear flow in T-section is shown below.
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As mentioned earlier for the asymmetric sections, shear center does not lie on the axes passing through the centroid. Consider a hollow square section with a cut at one of the corner. The centroid is at center but the section is not symmetric about any axes.
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Calculation for determining position of Shear Center :-
Consider the following example of channel section.
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To determine the position of shear center, equilibrium of moment about the centroid is applied as shown below. For deciding the sign of bending moment, the direction of shear flow needs to be referred.
![]()
Shear Center is a point through which if the external load passes, then there will not be any twisting of the section. In other words, section will only be subjected to bending. It won't be subjected to Torsion.
In general, Shear center lies on the axis of symmetry. So for doubly symmetric section shear center lies at the intersection of the two axes of symmetry. Thus for doubly symmetric sections, shear center coincides with the centroid. If the section has only one axis of symmetry then shear center will lie on that axis at distance eccentric to the non-symmetric axis.
In order to determine the position of shear center, the direction of shear flow in a section needs to be known. For most of the regular sections the shear flow is smooth and logical. In other words, the direction of shear flow doesn't get changed abruptly. There are examples where the direction of shear flow changes abruptly.
Some important points :-
1) Shear is taken up by the elements which are parallel to the direction of applied shear.
2)The direction of shear flow in the elements parallel to the applied shear is always in opposite direction to that of applied shear.
3) For a shear acting in the direction parallel to the axis of symmetry, there will be point/s where shear flow will either converge or diverge. Such points can either be called as source or sink. Such points are located at the intersection of the axis of symmetry (passing through the centroid) with the section.
4)The value of shear flow is zero at the points where cross section is open to air.
In the following image below, shear flow is shown in various sections.
The corresponding shear flow diagram or Q(1st moment of area) diagram is attached below.
The shear flow in T-section is shown below.
As mentioned earlier for the asymmetric sections, shear center does not lie on the axes passing through the centroid. Consider a hollow square section with a cut at one of the corner. The centroid is at center but the section is not symmetric about any axes.
Calculation for determining position of Shear Center :-
Consider the following example of channel section.
To determine the position of shear center, equilibrium of moment about the centroid is applied as shown below. For deciding the sign of bending moment, the direction of shear flow needs to be referred.
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Undo
Shear centre is a point from which a concentrated load passes then there will be only bending and no twisting .Its also called centre of flexure. Its that point through which the resultant of shear passes.
Calculation of shear centre generally involves if you want to know the exact solution its generally a two to three page solution but there are simple tricks which can give an idea where can the shear centre can lie
- For a channel section it lies outside the frame of the channel section
- For L section it lies at the intersection of the two legs.
- For a symmetrical I section it lies at the centre of the section.
- For open section such as semicircular section and open circular slit it lies outside the section.
- for detailed solution one can visit this site SHEAR CENTRE -WITH EXAMPLES
In other languages
日本語で入力: せん断中心 の計算法を教えてもらえますか？