Black dot shown in the figure qualitatively represents the shear centre of the angle section. The option which represents the position of the shear centre is:

Question

What is the CORRECT match between the air pollutants and treatment techniques given in the table

Air Pollutants		Treatment techniques
P	NO₂	i	Flaring
Q	SO₂	ii	Cyclonic separator
R	CO	iii	Lime scrubbing
S	Particles	iv	NH₃ injection

Answer 1

Think about shear flow in each leg separately and where their lines of action must meet, rather than quoting the location rule directly.

Why an angle section needs a shear centre check: the angle section is an open thin-walled shape with no line of symmetry passing through both legs equally for a general unequal angle, so a shear load applied at the centroid would twist the section. The load must instead pass through the shear centre to produce pure bending with no twist.
Shear flow in a single thin flat leg: in a thin flat plate, shear flow can only run along the length of the plate, in the plane of the plate's mid-thickness surface. It cannot develop any shear flow across the thickness. So the resultant shear force carried by one leg acts along a line passing through that leg's own mid-thickness line.
Combine both legs: the angle section is just two such thin legs joined at a corner. The total resultant shear force is the sum of the two legs' individual resultants, and for the twisting effect to vanish, this combined resultant must pass through the point where the two legs' individual lines of action, their mid-thickness centre lines, cross.
Where do the centre lines cross: for a horizontal leg and a vertical leg meeting at a corner, their mid-thickness centre lines are a horizontal line and a vertical line, and these two lines intersect essentially right at the inner corner (heel) of the angle, not away from the section in open space and not on the outer edge of a leg.

So the shear centre sits at the intersection of the two legs' centre lines, at the corner of the angle. Among the four figures, only the option placing the black dot at that intersection point is correct.

The correct position of the shear centre is shown in option (D).

Answer 2

Think about shear flow in each leg separately and where their lines of action must meet, rather than quoting the location rule directly.

Why an angle section needs a shear centre check: the angle section is an open thin-walled shape with no line of symmetry passing through both legs equally for a general unequal angle, so a shear load applied at the centroid would twist the section. The load must instead pass through the shear centre to produce pure bending with no twist.
Shear flow in a single thin flat leg: in a thin flat plate, shear flow can only run along the length of the plate, in the plane of the plate's mid-thickness surface. It cannot develop any shear flow across the thickness. So the resultant shear force carried by one leg acts along a line passing through that leg's own mid-thickness line.
Combine both legs: the angle section is just two such thin legs joined at a corner. The total resultant shear force is the sum of the two legs' individual resultants, and for the twisting effect to vanish, this combined resultant must pass through the point where the two legs' individual lines of action, their mid-thickness centre lines, cross.
Where do the centre lines cross: for a horizontal leg and a vertical leg meeting at a corner, their mid-thickness centre lines are a horizontal line and a vertical line, and these two lines intersect essentially right at the inner corner (heel) of the angle, not away from the section in open space and not on the outer edge of a leg.

So the shear centre sits at the intersection of the two legs' centre lines, at the corner of the angle. Among the four figures, only the option placing the black dot at that intersection point is correct.

The correct position of the shear centre is shown in option (D).

Black dot shown in the figure qualitatively represents the shear centre of the angle section. The option which represents the position of the shear centre is:

Show Hint

The Correct Option is D

Solution and Explanation

Questions Asked in GATE CE exam