Civil engineering is the art and science of designing and building structures such as houses, bridges, dams, and skyscrapers. Our design methods, however, have not always been as advanced as they are today. Over centuries, engineers have learned from both successes and failures, while gradually applying mathematics to improve safety and efficiency.
The evolution of design philosophies reflects humanity’s growing understanding of strength, safety, and uncertainty in construction. Each new philosophy was introduced to address the shortcomings of the current one. With every step, the role of mathematics became more sophisticated, moving from simple empirical rules to probability-based models.
Historical development of design methods, the growing involvement of mathematics, and their adoption in international standards as well as Indian codes are presented below.
Vishwakarma is considered as the god of engineers, architects, and craftsmen. He is considered the architect and chief engineer of the gods, credited with constructing their heavenly abodes, celestial weapons and chariots.
In the early stages of engineering, structures were designed based on experience and rules of thumb. Builders used proportions observed from successful structures like arches, bridges, and cathedrals. Mathematics was minimal, usually limited to geometry and simple arithmetic.
Limitation: While useful for traditional materials such as stone and timber, empirical design could not ensure safety for modern materials like steel and reinforced concrete.
Builders relied mostly on experience and tradition. The Egyptians built the pyramids (around 2500 BC), the Romans built aqueducts and the Colosseum (around 100 AD). Structures were massive and heavy.
The Renaissance initiated interest in science and mathematics. Galileo (1638) studied the strength of beams. Robert Hooke (1678) discovered the law of elasticity (“Hooke’s Law”: extension is proportional to force). Engineers began to understand how loads and forces act on materials.
Industrial Revolution: bridges, railways, factories. Many new materials like steel were used, but also many failures occurred. Example: The Tay Bridge Disaster (Scotland, 1879) collapsed in a storm, killing 75 people. To avoid failures, engineers introduced the idea of a Factor of Safety (FoS).
WSM assumes that both material stress and structural response remain within the elastic range. Safety is ensured by applying a factor of safety (FoS) to the yield or ultimate strength.
Mathematics: Linear elastic theory, simple stress–strain relations, service load analysis.
WSM often gave uneconomical sections because the FoS was uniform and did not reflect different uncertainties in loads and material strengths.
ULM was introduced to achieve more economical designs. Instead of service loads, factored (increased) loads were considered and compared against the ultimate capacity of the member.
Mathematics: Nonlinear stress–strain curves, plastic theory, ultimate strength analysis.
ULM focused only on collapse safety and ignored serviceability aspects such as deflection and cracking.
LSM combined the strengths of WSM and ULM. It introduced different categories of limit states:
Loads and material strengths were treated with different partial safety factors.
Mathematics: Probability concepts introduced indirectly, statistical calibration of load and resistance factors.
Partial safety factors are semi-probabilistic, based on judgment and calibration. They do not fully reflect probability of failure.
Probability theory is used to directly quantify the safety level. Instead of fixed safety factors, the design ensures a target reliability index (β), which corresponds to a very small probability of failure (Pf).
Mathematics: Advanced statistics, probability distributions, reliability index (β), Monte Carlo simulation, stochastic models.
The evolution of design philosophies shows a gradual shift:
Each step required deeper mathematical sophistication, from simple elastic theory to nonlinear plastic theory, and finally to probability and statistics. International and Indian standards reflect this progression, with current research pointing towards full adoption of reliability-based methods in the future.