Home » Mechanical Engineering » Strength of Materials

Deflection in closely coiled helical springs: effect of number of turns Two closely coiled helical springs A and B are identical in all respects except that spring A has half as many turns as spring B. Find the ratio of their deflections δ<sub>A</sub>/δ<sub>B</sub> under the same load. Choose the correct value.

Q: Deflection in closely coiled helical springs: effect of number of turns Two closely coiled helical springs A and B are identical in all respects except that spring A has half as many turns as spring B. Find the ratio of their deflections δ A</s…

Formula Deflection of a close-coiled helical spring: δ = (8 P D³ n)/(G d⁴). For identical D, d, G and same load P, δ ∝ n. Apply If nA = ½ nB, then δA/δB = nA/nB = 1/2. Final Answer 1/2

Difficulty: Easy

Correct Answer: 1/2

Explanation:

Formula
Deflection of a close-coiled helical spring: δ = (8 P D³ n)/(G d⁴). For identical D, d, G and same load P, δ ∝ n.

Apply
If n_A = ½ n_B, then δ_A/δ_B = n_A/n_B = 1/2.

Final Answer
1/2

← Previous Question Next Question→

More Questions from Strength of Materials

Power transmission and shaft sizing: compare diameters for equal power at different speeds Two circular shafts 'A' and 'B' transmit the same power. Shaft 'A' runs at 250 rpm and shaft 'B' runs at 300 rpm. Decide which shaft must have the larger diameter (same material and allowable shear stress assumed). Choose the correct statement.
Thermal stress due to cooling: nature of stress developed in a bar cooled to −5°C A straight uniform bar is cooled down to −5°C. Assume the bar's ends are fully restrained against axial movement so that free contraction cannot occur. Identify the nature of stress developed due to cooling.
Hooke's law within elastic limit: relation between stress and strain For a material loaded within its elastic (proportional) limit, state how stress varies with strain. Choose the most appropriate completion.
Bending theory: stress at the neutral axis of a beam cross-section Define the neutral axis of a beam cross-section under pure bending. Identify the bending stress value at the neutral axis.
Tension test terminology: stress level where extension accelerates with small load increase From a standard stress–strain curve in tension, identify the stress at which the extension increases more rapidly than the increase in load.
Elastic energy terms: identify correct statements about strain energy, proof resilience, and modulus of resilience Consider the standard definitions used in strength of materials. Select the correct group of statements.
Beam theory: meaning of point of contraflexure (inflection point) On a bending moment diagram for a beam, identify what occurs at the point of contraflexure.
Solid circular shaft: torque–diameter relation at allowable shear stress For a solid circular shaft of diameter D, limited by maximum allowable shear stress τ, state the formula for the maximum torque transmitted.
Stability of columns: applicability of Euler's buckling formula State for which type of column Euler's critical load formula is valid, based on slenderness.
Plane stress analysis: compute the maximum normal stress (principal stress) for a biaxial state with shear A body is under σ_x = 1200 MPa (tension) and σ_y = 600 MPa (tension) on mutually perpendicular planes. A shear stress τ_xy = 400 MPa acts on the same planes. Determine the maximum principal (normal) stress.

Discussion & Comments

No comments yet. Be the first to comment!

Join Discussion