Question

A concrete pillar, which is reinforced with steel rods, supports a compressive axial load of 2 MN.

(a) Determine stresses σ₁ and σ₂ given the following: 

For the steel, A₁ = 4 × 10⁻³ m² and E₁ = 2 × 10¹¹ N/m²

For the concrete, A₂ = 0.2 m² and E₂ = 2 × 10¹⁰ N/m²

(b) What percentage of the total load does the steel reinforcement take? 

Answer 1

(a) 

From the above equation

i.e. the stress in the steel,

σ₁ = −83.3 MPa   ........(1.10)

From the above equation

i.e. the stress in the concrete, 

σ₂ = −8.3 MPa   .......(1.11)

(b) Force in the steel,

F₁ = σ₁A₁

= −83.3 × 10⁶ × 4 × 10⁻³ 

= 3.33 × 10⁵ N

Therefore, the percentage total load taken by the steel reinforcement