Day 24-Oct 11-worksheet-Btech coaching-Design of torsion

When a rectangular RCC beam is subjected to pure torsion, the shape of principal tensile stress trajectories is—

• Parabolic

• Radial

• Helical

• Circular

A solid rectangular section (b = 300 mm, D = 450 mm) resists a torsional moment of T_u = 20 kN m. It experiences pure torsion.What is the equivalent shear V_e ?

• 21.5 kN

• 240 kN

• 106.67 kN

• 300.9 kN

Answer explanation

1. Formula → V_e = 1.6 × T_u / b (for pure torsion)

2. Substitute → V_e = 1.6 × (20 × 10⁶) / 300 = 106 667 N

3. Answer → V_e = 106.7 kN

For combined bending + torsion, the design longitudinal reinforcement must resist—

• M_u only

• M_t only

• (M_u ± M_t) whichever greater

• M_u + T_u / 1.7

If Tu / (1.7 bD) > τc,max for concrete grade, the member shall be—

• Reduce number of steel

• Redesigned with larger section

• Ignored for torsion

• Avoid stirrups

For a beam 250 × 400 mm (M25, Fe500) carrying Tu = 15 kN m, find Mt.

• 5.2 kN m

• 69 kN m

• 23 kN m

• 85 kN m

Answer explanation

1. Formula: Mt = Tu × (1 + D/b) / 1.7

2. Substitute: b=250 mm, D=400 mm → (1 + 400/250)=2.6

3. Mt = 15 × 2.6 / 1.7 = 22.94 kN·m (≈ 23 kN·m)

Under torsion, the maximum tensile stress acts on the diagonal planes inclined at 45° to the longitudinal axis.

• True

• False

When torsion acts simultaneously with shear, the equivalent shear stress τe = (τv + τt).

• True

• False

Assertion (A): Torsional reinforcement is placed near the corners of rectangular sections. Reason (R): Because the minimum shear flow due to torsion occurs at the perimeter of the section.

• Both A and R true, R explains A.

• Both A and R true, R not explanation.

• A true, R false.

• A false, R true.

Answer explanation

Because the maximum shear flow due to torsion occurs at the perimeter of the section.

In RCC members, torsional shear stress τt varies linearly from zero at the _______ to maximum at the surface.

The equivalent bending moment for torsion is given by Mt = (Tu / 1.7) × (1 + ____ / ____).