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 (a)   to maximum at the surface.

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

(a)