BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE PILANI
FIRST SEMESTER 2025-2026
Design of Machine Elements (ME F314/MF F314)
3rd November 2025
Tutorial Test #4
Duration: 50 mins
Q1. A semi-elliptic spring used for an automobile suspension consists of three extra full-length
leaves and nine graduated-length leaves (including the master leaf). The centre-to-centre distance
between the two eyes is 1.15 m. The leaves are made of spring steel 60Si2CrVA with yield strength
Syt = 1350 MPa and modulus E = 210 GPa. A factor of safety of 2.0 is specified. The maximum
spring load on one spring is 26 kN. The leaves are pre-stressed (nipped) so as to equalize stresses
in all leaves under the maximum load. Neglect eye and band thicknesses.
Determine:
(a) The dimensions of the cross-section of the leaves (b × t), choosing practical integer values in
mm.
(b) The deflection at the end of the spring at the maximum load.
(c) The spring rate 𝑘(N/mm) of one spring when all leaves are active (ignore interleaf friction).
Important formulae are given at the back.
Important Formula
Bending stress formula for multiple leaf strings without prestress.
Deflection
Nip
Preload.
Maximum bending stress when preload is applied.