When a static load (P) is applied at the end (B) of a uniform metal rod that is fixed at the other end (A), the rod experiences elongation. According to the mechanics of materials, this elongation (Δl) can be calculated using the formula Δl = (P * L) / (A * E), where:
- P is the static load applied at the free end of the rod.
- L is the original length of the rod.
- A is the cross-sectional area of the rod.
- E is the modulus of elasticity of the material of the rod.
This formula indicates that the increase in length of the rod is directly proportional to the applied load (P) and the original length (L), while being inversely proportional to the cross-sectional area (A) and the modulus of elasticity (E). Thus, a higher load or longer rod will result in greater elongation, while a larger cross-sectional area and a stiffer material (higher E) will reduce the elongation.