Cost comparison of materials for a tie rod

The tie rod is in simple tension, so the required area is $A = \dfrac{P \times FS}{S_y}$, mass $m = \rho A L$ and cost $= m \times$ price.

Given: $P = 50\ \text{kN}$, $FS = 2$, $L = 1\ \text{m}$. Design load $= 50 \times 2 = 100\ \text{kN}$.

Area, mass and cost

For mild steel:

$$\begin{aligned} A &= \frac{100\,000}{250} = 400\ \text{mm}^2 \\ m &= 7850 \times 400\times10^{-6} \times 1 = 3.14\ \text{kg} \\ \text{Cost} &= 3.14 \times 120 = \text{Rs } 377 \end{aligned}$$

The other materials are worked out in the same way:

Comment

• Cheapest: alloy steel 4140 (about Rs 217), although its price per kg is higher than mild steel, because its higher strength needs much less material.
• Lightest: titanium alloy (0.50 kg), but it costs about seven times as much as 4140, so it is justified only where weight is critical (aircraft, aerospace).
• Price per kg alone is misleading; the cost should be compared on the basis of the function performed (cost per unit strength, or cost of the finished part). Machining, joining, corrosion protection, availability and the cost of a heavier structure supporting the part must also be included.
• For stiffness-limited or buckling-limited parts the comparison would use modulus, and the ranking can change.

Answer: Cheapest = alloy steel 4140 (Rs 217, 1.21 kg); lightest = Ti-6Al-4V (0.50 kg, Rs 1510).