In Indian Railway track design for timber sleepers: if S is the strength index and H is the hardness index of the timber (both evaluated at 12% moisture content), what is the composite sleeper index (CSI) used for suitability comparison?

Introduction / Context:
The composite sleeper index (CSI) is a simple, widely cited metric in railway engineering for comparing different timber species for sleepers. It combines two essential material characteristics—strength and hardness—measured at a standardized 12% moisture content to reflect field conditions for track components.

Given Data / Assumptions:

• S = strength index of the timber at 12% moisture content.
• H = hardness index of the timber at 12% moisture content.
• Both indices are dimensionless comparative measures derived from standard tests.

Concept / Approach:

Sleepers demand adequate bending strength to resist rail-seat loads and sufficient hardness to withstand crushing and wear from fastenings and rail bearing. A composite index that multiplies these factors reflects that a poor value in either strength or hardness significantly degrades overall performance; hence a product (not a sum) better captures combined adequacy.

Step-by-Step Solution:

Verification / Alternative check:

For two timbers: Timber A (S=100, H=70) vs Timber B (S=85, H=85). Although sums are equal (170), product favors the more balanced timber: 100×70 = 7000 vs 85×85 = 7225, aligning with engineering intuition that balance is desirable.

Why Other Options Are Wrong:

CSI = S + H ignores interaction; (S × H)/100 is merely a scaled form without standard practice; S/H or 2S + H distort relative influence and provide no accepted engineering basis.

Common Pitfalls:

Using indices at moisture levels other than 12% or mixing test standards; comparing species without accounting for preservative treatability and service conditions.

Final Answer:

CSI = S × H