Q.A reinforced concrete beam 300 mm wide by 550 mm overall depth is reinforced with 4 bars of 20mm diameter at an effective depth of 500 mm. Using M 20 grade concrete and Fe 415 steel, estimate the moment of resistance of the section.
Q. A reinforced concrete beam 250 mm wide by 475 mm overall depth is reinforced with 3 bars of 16mm diameter at an effective cover of 50 mm. Using M 20 grade concrete and Fe 415 steel, find the depth of neutral axis.
SOLUTION:
WIDTH b= 250mm
EFFECTIVE DEPTH d = 475 – 50 = 425mm
AREA OF TENSION STEEL Ast = 3× π /4 ×16² = 603.2mm²
1. PERMISSIBLE STRESSES.
σcbc = 7 N/mm²
σst = 230 N/mm²
2. MODULAR RATIO
m = 280/3σcbc
= 280/ 3×7
= 13.33
3. DEPTH OF NEUTRAL AXIS
Equating the moments of areas of compression and tension zone about the neutral axis
bn²/2= m.Ast(d – n)
1/2×250 n² = 13.33 x 603.2 (425 – n)
125 n² = 3.42×10⁶ – 8040.7 n
n² +64.33 n – 27360= O
n= (- 64.33 + √64.33² +4 × 27360)/2
n = 136.3 mm
DEPTH OF NEUTRAL AXIS n = 136.3 mm
Q.A reinforced concrete beam 300 mm wide by 550 mm overall depth is reinforced with 4 bars of 20mm diameter at an effective depth of 500 mm. Using M 20 grade concrete and Fe 415 steel, estimate the moment of resistance of the section.
SOLUTION:
WIDTH b= 300mm
EFFECTIVE DEPTH d = 550 – 50 = 500mm
AREA OF TENSION STEEL Ast = 4× π /4 ×20² = 1256.6mm²
1. PERMISSIBLE STRESSES.
σcbc = 7 N/mm²
σst = 230 N/mm²
2. MODULAR RATIO
•m = 280/3σcbc
= 280/ 3×7
= 13.33
•Critical depth of neutral axis NC = 0.289d
3. DEPTH OF NEUTRAL AXIS
Equating the moments of areas of compression and tension zone about the neutral axis
bn²/2= m.Ast(d – n)
1/2×300 n² = 13.33 x 1256.6 (500 – n)
150 n² = 8.375×10⁶ – 16750.5 n
n² +111.7 n – 55840= O
n= (- 111.7 + √111.7² +4 × 55840)/2
n = 187 mm
critical depth of neutral axis Nc= 0.289×500 = 144.5mm
