Centroid of a standard T-section (10 × 15 × 5 cm) A T-section has flange 10 cm wide and 5 cm thick, with a web (stem) 5 cm thick and 10 cm deep beneath the flange (overall depth 15 cm). Measured from the bottom of the section, locate the centroid (distance ȳ).

Introduction / Context:Locating the centroid (center of gravity for uniform density) of built-up sections such as T-sections is a staple of structural analysis. It involves dividing the shape into simple rectangles, using the first moment of area about a reference line, and then finding the combined centroidal location.

Given Data / Assumptions:

• Flange: width b_f = 10 cm, thickness t_f = 5 cm.
• Web (stem): thickness b_w = 5 cm, depth h_w = 10 cm below flange.
• Bottom reference at the base of the stem; overall depth = 15 cm.
• Uniform density and thickness; ignore fillets.

Concept / Approach:

Use composite areas. The centroid measured from the chosen reference is ȳ = Σ(A_i y_i) / ΣA_i, where A_i are component areas and y_i are their centroidal distances from the reference. Take two rectangles: web and flange.

Step-by-Step Solution:

Verification / Alternative check:

Symmetry about the vertical axis through the stem confirms x̄ is centered; the ȳ value lies between 5 and 12.5 cm, which is reasonable for equal flange and web areas.

Why Other Options Are Wrong:

5.00 cm and 7.50 cm are too low; 7.85 cm is also low; “None” is incorrect because the calculation yields 8.75 cm exactly for the stated geometry.

Common Pitfalls:

Misinterpreting the given 10 × 15 × 5 cm as a solid rectangle; forgetting to reference centroid distances consistently from the same datum; arithmetic slips in Σ(A y).

Final Answer:

8.75 cm