If a Column has been design with a cross sectional area of 120,000 mm² is subject to an axial load of 2,500 KN and a diameter of the steel to be 25mm determine the steel stress in both the steel and concrete if the elastic modulus of the steel and concrete are 200 KN/mm² and 21 KN/mm² respectively

Question

Asked on August 10, 2026Physics

This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.

Accepted Answer · 2026-08-10T23:10:36.753Z

To determine the stress in both the steel stud and the concrete, we will use the principles of composite sections under axial load. The key is that both materials experience the same strain, and the total load is shared between them. Given: Total cross-sectional area of column, A_total = 120,000 mm^2 Axial load, P = 2,500 KN Diameter of steel bar, d_s = 25 mm Elastic modulus of steel, E_s = 200 KN/mm^2 Elastic modulus of concrete, E_c = 21 KN/mm^2 Assumption: The problem implies a single steel reinforcing bar (stud) with a diameter of 25 mm. Step 1: Calculate the cross-sectional area of the steel stud (A_s). The area of a circular bar is given by A = ( d^2)/(4). A_s = (25 mm)^24 = ( × 625)/(4) mm^2 ≈ 490.87 mm^2 Step 2: Calculate the cross-sectional area of the concrete (A_c). The total area of the column is the sum of the steel area and the concrete area. A_c = A_total - A_s = 120,000 mm^2 - 490.87 mm^2 = 119,509.13 mm^2 Step 3: Calculate the modular ratio (n). The modular ratio is the ratio of the elastic moduli of steel to concrete. n = (E_s)/(E_c) = 200 KN/mm^221 KN/mm^2 ≈ 9.5238 Step 4: Determine the stress in the concrete (_c). For a composite section under axial load, the total load P is distributed between the concrete and steel. The strain in both materials is equal (_s = _c). We know that = E , so _s = E_s and _c = E_c . This implies _s = (E_s)/(E_c) _c = n _c. The total load P = P_c + P_s = _c A_c + _s A_s. Substitute _s = n _c: P = _c A_c + (n _c) A_s = _c (A_c + n A_s) Now, solve for _c: _c = (P)/(A_c + n A_s) Substitute the values: _c = 2,500 KN119,509.13 mm^2 + (9.5238 × 490.87 mm^2) _c = 2,500 KN119,509.13 mm^2 + 4675.00 mm^2 _c = 2,500 KN124,184.13 mm^2 _c ≈ 0.02013 KN/mm^2 Step 5: Determine the stress in the steel stud (_s). Using the relationship _s = n _c: _s = 9.5238 × 0.02013 KN/mm^2 _s ≈ 0.1917 KN/mm^2 The stresses are: Stress in concrete: 0.02013 KN/mm^2 Stress in steel stud: 0.1917 KN/mm^2 Send me the next one 📸

Accepted Answer · 2026-08-10T23:10:36.753Z

To determine the stress in both the steel stud and the concrete, we will use the principles of composite sections under axial load. The key is that both materials experience the same strain, and the total load is shared between them. Given: Total cross-sectional area of column, A_total = 120,000 mm^2 Axial load, P = 2,500 KN Diameter of steel bar, d_s = 25 mm Elastic modulus of steel, E_s = 200 KN/mm^2 Elastic modulus of concrete, E_c = 21 KN/mm^2 Assumption: The problem implies a single steel reinforcing bar (stud) with a diameter of 25 mm. Step 1: Calculate the cross-sectional area of the steel stud (A_s). The area of a circular bar is given by A = ( d^2)/(4). A_s = (25 mm)^24 = ( × 625)/(4) mm^2 ≈ 490.87 mm^2 Step 2: Calculate the cross-sectional area of the concrete (A_c). The total area of the column is the sum of the steel area and the concrete area. A_c = A_total - A_s = 120,000 mm^2 - 490.87 mm^2 = 119,509.13 mm^2 Step 3: Calculate the modular ratio (n). The modular ratio is the ratio of the elastic moduli of steel to concrete. n = (E_s)/(E_c) = 200 KN/mm^221 KN/mm^2 ≈ 9.5238 Step 4: Determine the stress in the concrete (_c). For a composite section under axial load, the total load P is distributed between the concrete and steel. The strain in both materials is equal (_s = _c). We know that = E , so _s = E_s and _c = E_c . This implies _s = (E_s)/(E_c) _c = n _c. The total load P = P_c + P_s = _c A_c + _s A_s. Substitute _s = n _c: P = _c A_c + (n _c) A_s = _c (A_c + n A_s) Now, solve for _c: _c = (P)/(A_c + n A_s) Substitute the values: _c = 2,500 KN119,509.13 mm^2 + (9.5238 × 490.87 mm^2) _c = 2,500 KN119,509.13 mm^2 + 4675.00 mm^2 _c = 2,500 KN124,184.13 mm^2 _c ≈ 0.02013 KN/mm^2 Step 5: Determine the stress in the steel stud (_s). Using the relationship _s = n _c: _s = 9.5238 × 0.02013 KN/mm^2 _s ≈ 0.1917 KN/mm^2 The stresses are: Stress in concrete: 0.02013 KN/mm^2 Stress in steel stud: 0.1917 KN/mm^2 Send me the next one 📸

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