Plastic Analysis MCQ with answer and solution

Concept

The geometrical neutral axis passes through the centroid of the cross-section, whereas the plastic neutral axis divides the total area of the cross-section into two equal halves.

Formula

y_bar = (A1·y1 + A2·y2) / (A1 + A2)

Step-by-step solution

1. Understand the T-section dimensions: Flange width b_f = 400 mm, Flange thickness t_f = 100 mm, Web width b_w = 100 mm, Overall depth D = 600 mm, Web depth d_w = 500 mm. 2. Calculate the total area (A) and centroid (GNA) from the top fiber: Area of flange (A_f) = 400 × 100 = 40,000 mm² Area of web (A_w) = 100 × 500 = 50,000 mm² Total Area = 90,000 mm² Centroid from top fibre (y_bar) = [(40000 × 50) + (50000 × (100 + 250))] / 90000 = [2,000,000 + 17,500,000] / 90000 = 19,500,000 / 90000 = 216.67 mm ≈ 217 mm. 3. Calculate the Plastic Neutral Axis (PNA): Total Area / 2 = 90,000 / 2 = 45,000 mm². Area of the flange = 40,000 mm² (which is less than 45,000 mm²). Therefore, PNA lies within the web, just below the flange. Let y_p be the depth of PNA from the top fiber. Area of flange + Area of web portion up to PNA = 45,000 mm² 40,000 + b_w × (y_p - t_f) = 45,000 40,000 + 100 × (y_p - 100) = 45,000 100 × (y_p - 100) = 5,000 y_p - 100 = 50 y_p = 150 mm.

Explanation