RCC Numerical – calculate moment of resistance of the section.

A singly reinforced concrete beam 200 mm width and having effective depth 350 mm is reinforced with 3 bars of 12 mm diameter. Using M15 concrete of Fe415 steel, calculate moment of resistance of the section.

To calculate the moment of resistance of a singly reinforced concrete beam, we use the following steps:

Given Data:

• Width of the beam (b) = 200 mm
• Effective depth (d) = 350 mm
• Reinforcement = 3 bars of 12 mm diameter
• Concrete grade = M15 (i.e., 𝑓𝑐𝑘=15 N/mm²)
• Steel grade = Fe415 (i.e., 𝑓𝑦=415 N/mm²)

Step 1: Calculate the Area of Steel (A𝑠𝑡)

For 3 bars of 12 mm diameter:

𝐴𝑠𝑡=3×𝜋4×(12)2=3×𝜋4×144=3×113.097=339.292 mm2

Step 2: Calculate the Neutral Axis (x𝑢)

Using the formula for the neutral axis for singly reinforced sections:

𝑥𝑢=0.87𝑓𝑦𝐴𝑠𝑡0.36𝑓𝑐𝑘𝑏

Substitute the values:

𝑥𝑢=0.87×415×339.2920.36×15×200𝑥𝑢=122,804.0161080=113.705 mm

Step 3: Calculate Limiting Depth of Neutral Axis (x𝑢𝑚𝑎𝑥)

For Fe415 steel, the limiting depth of the neutral axis is:

𝑥𝑢𝑚𝑎𝑥=0.48×𝑑=0.48×350=168 mm

Since 𝑥𝑢<𝑥𝑢𝑚𝑎𝑥, the section is under-reinforced.

Step 4: Calculate Moment of Resistance (M𝑅)

The moment of resistance is given by:

𝑀𝑅=0.87𝑓𝑦𝐴𝑠𝑡(𝑑−0.42𝑥𝑢1000)

Substitute the values:

𝑀𝑅=0.87×415×339.292×(350−0.42×113.705)/1000𝑀𝑅=122,804.016×(350−47.757)/1000𝑀𝑅=122,804.016×302.243/1000𝑀𝑅=37,100,384.54/1000=37.1 kNm

Final Answer:

The moment of resistance of the section is 37.1 kNm.