Limit State Method MCQ with answer and solution

Concept

Stress Block Parameters in Limit State Method

Formula

Ratio = (3/7 × xu) / (4/7 × xu) = 3/4

Step-by-step solution

1. Identify the depth of the rectangular stress block as (3/7)xu and the parabolic stress block as (4/7)xu. 2. Divide the rectangular block depth by the parabolic block depth: (3/7 \* xu) / (4/7 \* xu). 3. Cancel out xu to get (3/7) / (4/7) = 3/4.

Explanation

In the limit state method, the concrete stress block in compression is divided into two parts: a top rectangular portion of depth (3/7)xu and a bottom parabolic portion of depth (4/7)xu, where xu is the neutral axis depth. The ratio of the depth of the rectangular stress block to the parabolic stress block is (3/7) / (4/7) = 3/4.

Shortcut

Remember the depth breakdown from top to bottom as 3/7 (Rectangular) and 4/7 (Parabolic). Since both share the same denominator (7), the ratio of Rectangular to Parabolic depth is simply 3:4 or 3/4.

Common mistake

Students often confuse the depth of the rectangular portion (3/7) or the parabolic portion (4/7) with the ratio of the two portions, or invert the ratio to 4/3 (parabolic to rectangular) instead of calculating rectangular to parabolic (3/4).