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If the permissible compressive stress in concrete in bending for M30 grade of concrete is 10 N/mm2, then modular ratio will be
- a)18.66
- b)13.33
- c)10.98
- d)9.33
Correct answer is option 'D'. Can you explain this answer?
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If the permissible compressive stress in concrete in bending for M30 g...
As per IS : 456-2000, modular ratio is given by
For M30 concrete
σcbc = 10 N/mm2
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If the permissible compressive stress in concrete in bending for M30 g...
Permissible Compressive Stress in Concrete in Bending
The given question states that the permissible compressive stress in concrete in bending for M30 grade of concrete is 10 N/mm2.
Modular Ratio
Modular ratio is defined as the ratio of the modulus of elasticity of steel to that of concrete. It is denoted by m.
Formula for Modular Ratio
m = Es/Ec
Where,
Es = Modulus of elasticity of steel
Ec = Modulus of elasticity of concrete
Modulus of Elasticity of Steel and Concrete
The modulus of elasticity of steel is 2.0 x 105 N/mm2.
The modulus of elasticity of concrete can be calculated using the following formula:
Ec = 5000 √fc
Where,
fc = Characteristic compressive strength of concrete in N/mm2
For M30 grade of concrete, the characteristic compressive strength is 30 N/mm2.
Therefore,
Ec = 5000 √30 = 13,333 N/mm2
Substituting the values in the formula for modular ratio:
m = Es/Ec = 2.0 x 105/13,333 = 15
Permissible Compressive Stress in Concrete in Bending and Modular Ratio
The permissible compressive stress in concrete in bending for M30 grade of concrete is 10 N/mm2.
Using the formula for modular ratio:
m = Es/Ec = 15
The formula for permissible compressive stress in concrete in bending is:
σcbc = σst/m
Where,
σcbc = Permissible compressive stress in concrete in bending
σst = Permissible tensile stress in steel
Assuming the permissible tensile stress in steel to be 140 N/mm2:
σcbc = σst/m = 140/15 = 9.33 N/mm2
Therefore, the modular ratio will be 9.33 (option D).
The given question states that the permissible compressive stress in concrete in bending for M30 grade of concrete is 10 N/mm2.
Modular Ratio
Modular ratio is defined as the ratio of the modulus of elasticity of steel to that of concrete. It is denoted by m.
Formula for Modular Ratio
m = Es/Ec
Where,
Es = Modulus of elasticity of steel
Ec = Modulus of elasticity of concrete
Modulus of Elasticity of Steel and Concrete
The modulus of elasticity of steel is 2.0 x 105 N/mm2.
The modulus of elasticity of concrete can be calculated using the following formula:
Ec = 5000 √fc
Where,
fc = Characteristic compressive strength of concrete in N/mm2
For M30 grade of concrete, the characteristic compressive strength is 30 N/mm2.
Therefore,
Ec = 5000 √30 = 13,333 N/mm2
Substituting the values in the formula for modular ratio:
m = Es/Ec = 2.0 x 105/13,333 = 15
Permissible Compressive Stress in Concrete in Bending and Modular Ratio
The permissible compressive stress in concrete in bending for M30 grade of concrete is 10 N/mm2.
Using the formula for modular ratio:
m = Es/Ec = 15
The formula for permissible compressive stress in concrete in bending is:
σcbc = σst/m
Where,
σcbc = Permissible compressive stress in concrete in bending
σst = Permissible tensile stress in steel
Assuming the permissible tensile stress in steel to be 140 N/mm2:
σcbc = σst/m = 140/15 = 9.33 N/mm2
Therefore, the modular ratio will be 9.33 (option D).
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If the permissible compressive stress in concrete in bending for M30 grade of concrete is 10 N/mm2, then modular ratio will bea)18.66b)13.33c)10.98d)9.33Correct answer is option 'D'. Can you explain this answer?
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