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The dimensions for the flexural rigidity of a beam element in mass (M), length (L) and time (T) is given by:
- a)MT-2
- b)M-1T2
- c)ML-1T-2
- d)ML3T-2
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The dimensions for the flexural rigidity of a beam element in mass (M)...
In a beam, the flexural rigidity (EI) varies along the length as a function of x as shown in equation:
Where E is the young's modulus (in Pasual, Pa), I is the second moment of area (in m4). Y is the traverse displacement of the beam x and M(x) is the bending moment at x. The SI unit of flexural rigidity is thus Pa. m4 or Nm4
∴ Dimension is ML3T–2
Where E is the young's modulus (in Pasual, Pa), I is the second moment of area (in m4). Y is the traverse displacement of the beam x and M(x) is the bending moment at x. The SI unit of flexural rigidity is thus Pa. m4 or Nm4
∴ Dimension is ML3T–2
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The dimensions for the flexural rigidity of a beam element in mass (M)...
Flexural Rigidity of a Beam Element
Flexural rigidity of a beam element is one of the important properties of a beam that determines its ability to resist bending. It is defined as the product of the bending stiffness and the second moment of area of the beam.
Dimensions of Flexural Rigidity
The dimensions of flexural rigidity of a beam element are given in terms of mass (M), length (L) and time (T). The correct option among the given choices is (D) ML3T-2. Let us understand why.
- The bending stiffness of a beam is given by the product of the modulus of elasticity (E) and the moment of inertia (I) of the beam. Therefore, the dimensions of bending stiffness are ML2T-2.
- The second moment of area (I) of a beam is the measure of its resistance to bending. It is given by the integral of the product of the area and the square of the perpendicular distance between the centroid of the area and the neutral axis of the beam. Therefore, the dimensions of the second moment of area are L4.
- Hence, the dimensions of flexural rigidity, which is the product of bending stiffness and second moment of area, are ML2T-2 x L4 = ML3T-2.
Final Words
In conclusion, the correct dimensions of flexural rigidity of a beam element are ML3T-2. This property is important in designing and analyzing beam structures in civil engineering.
Flexural rigidity of a beam element is one of the important properties of a beam that determines its ability to resist bending. It is defined as the product of the bending stiffness and the second moment of area of the beam.
Dimensions of Flexural Rigidity
The dimensions of flexural rigidity of a beam element are given in terms of mass (M), length (L) and time (T). The correct option among the given choices is (D) ML3T-2. Let us understand why.
- The bending stiffness of a beam is given by the product of the modulus of elasticity (E) and the moment of inertia (I) of the beam. Therefore, the dimensions of bending stiffness are ML2T-2.
- The second moment of area (I) of a beam is the measure of its resistance to bending. It is given by the integral of the product of the area and the square of the perpendicular distance between the centroid of the area and the neutral axis of the beam. Therefore, the dimensions of the second moment of area are L4.
- Hence, the dimensions of flexural rigidity, which is the product of bending stiffness and second moment of area, are ML2T-2 x L4 = ML3T-2.
Final Words
In conclusion, the correct dimensions of flexural rigidity of a beam element are ML3T-2. This property is important in designing and analyzing beam structures in civil engineering.
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The dimensions for the flexural rigidity of a beam element in mass (M), length (L) and time (T) is given by:a)MT-2b)M-1T2c)ML-1T-2d)ML3T-2Correct answer is option 'D'. Can you explain this answer?
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