Which one of the following stress conditions represents the state of pure shear stress?

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

Pure shear means a stress element carries only shear stress on its faces, no direct normal stress at all, with the shear arrows on adjacent faces forming a self-balancing complementary pair. Check each figure against that rule.

Figure (A): all four faces carry shear stress of magnitude 40 acting tangentially, and the arrow directions rotate consistently around the element, so the moment from one pair of faces cancels the moment from the other pair. Zero normal stress, self-balanced couples: this is pure shear.
Figure (B): magnitude 40 tangential to each face again, but the direction on part of the element is flipped compared to (A). That flip breaks the complementary shear condition, so the couple produced would not cancel to zero, which cannot be a real equilibrium state.
Figure (C): same issue as (B), a different face has its arrow direction reversed relative to the correct complementary pattern, again failing rotational equilibrium.
Figure (D): the arrows point straight out of (or into) each face, perpendicular to it. That is a direct normal stress acting equally in the x and y directions, a case of biaxial normal stress, not shear stress, so it is ruled out immediately.

Once (D) is ruled out for showing normal stress instead of shear, and (B) and (C) are ruled out for violating the complementary-shear equilibrium requirement, (A) is the only figure left that is both purely shear and physically valid with zero net moment.

Let's summarize:

Pure shear needs zero normal stress on every face, equal-magnitude shear on all four faces, and complementary sense so the net moment is zero.
A normal-stress diagram like (D), or a shear diagram with a broken complementary pattern like (B) and (C), cannot represent pure shear.

The correct option is (A).

Answer 2

Pure shear means a stress element carries only shear stress on its faces, no direct normal stress at all, with the shear arrows on adjacent faces forming a self-balancing complementary pair. Check each figure against that rule.

Figure (A): all four faces carry shear stress of magnitude 40 acting tangentially, and the arrow directions rotate consistently around the element, so the moment from one pair of faces cancels the moment from the other pair. Zero normal stress, self-balanced couples: this is pure shear.
Figure (B): magnitude 40 tangential to each face again, but the direction on part of the element is flipped compared to (A). That flip breaks the complementary shear condition, so the couple produced would not cancel to zero, which cannot be a real equilibrium state.
Figure (C): same issue as (B), a different face has its arrow direction reversed relative to the correct complementary pattern, again failing rotational equilibrium.
Figure (D): the arrows point straight out of (or into) each face, perpendicular to it. That is a direct normal stress acting equally in the x and y directions, a case of biaxial normal stress, not shear stress, so it is ruled out immediately.

Once (D) is ruled out for showing normal stress instead of shear, and (B) and (C) are ruled out for violating the complementary-shear equilibrium requirement, (A) is the only figure left that is both purely shear and physically valid with zero net moment.

Let's summarize:

Pure shear needs zero normal stress on every face, equal-magnitude shear on all four faces, and complementary sense so the net moment is zero.
A normal-stress diagram like (D), or a shear diagram with a broken complementary pattern like (B) and (C), cannot represent pure shear.

The correct option is (A).

Which one of the following stress conditions represents the state of pure shear stress?

Show Hint

The Correct Option is A

Solution and Explanation

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