What is the formula for calculating the moment of inertia of a rectangular beam?
A (bh³) / 12
B (bh²) / 6
C (bh²) / 2
D (bh³) / 36
The moment of inertia (I) for a rectangular beam about its centroidal axis is I = (bh³) / 12, where b is the base width and h is the height. It measures the beam’s resistance to bending.
Which of the following is true for a statically determinate structure?
A It has redundant supports
B It requires compatibility equations
C It is always unstable
D It can be analyzed using equilibrium equations alone
A statically determinate structure can be fully analyzed using only the equations of equilibrium (sum of forces and moments equal to zero). It has no redundant supports.
What is the formula for calculating the critical buckling load of a column?
A (π²EI) / (KL)²
B EI / L²
C (π²EI) / KL²
D (EIπ²) / KL²
The critical buckling load (Pcr) for a column is given by Euler’s formula:
Pcr = (π²EI) / (KL)², where E is modulus of elasticity, I is moment of inertia, K is the effective length factor, and L is the length.
Which of the following is true for a simply supported beam with a point load at the center?
A Maximum bending moment occurs at the supports
B Maximum shear force occurs at the center
C Both a and b
D Maximum deflection occurs at the supports
For a simply supported beam with a point load at the center, the maximum bending moment occurs at the center, and the maximum shear force occurs at the supports.
What is the formula for calculating the strain energy in a spring?
A (1/2) kx²
B kx
C (1/2) mv²
D (1/2) Fx
The strain energy stored in a spring is given by U = (1/2) kx², where k is the spring constant and x is the displacement from the equilibrium position.
Which of the following is true for a cantilever beam with a point load at the free end?
A Maximum bending moment occurs at the free end
B Maximum shear force occurs at the free end
C Both a and b
D Maximum deflection occurs at the fixed end
For a cantilever beam with a point load at the free end, the maximum bending moment occurs at the fixed end, and the shear force is constant along the length of the beam.
What is the formula for calculating the modulus of elasticity?
A Strain / Stress
B Stress / Strain
C Force / Area
D Mass × Acceleration
The modulus of elasticity (E) is a material property defined as the ratio of stress to strain within the elastic limit. It measures the stiffness of a material.
Which of the following is true for a truss structure?
A It is made of curved members
B It carries bending moments
C It carries only axial loads
D It cannot carry tension
A truss structure consists of straight members connected at joints, and it carries only axial loads (tension or compression). It is designed to be lightweight and efficient.
What is the formula for calculating the shear stress in a beam?
A (VQ) / (It)
B V / A
C M / I
D F / A
The shear stress (τ) in a beam is calculated using the formula τ = (VQ) / (It), where V is shear force, Q is the first moment of area, I is moment of inertia, and t is thickness.
Which of the following is true for a free-body diagram?
A It shows only external forces
B It includes internal forces
C It ignores equilibrium
D It is used only for beams
A free-body diagram (FBD) is a graphical representation of all external forces acting on a body. It is used to analyze forces and moments in equilibrium problems.
What is the formula for calculating the center of mass?
A Sum of forces / Total mass
B Sum of moments / Total mass
C Sum of distances / Total volume
D Sum of areas / Total length
The center of mass (COM) is calculated as the sum of the moments of individual masses divided by the total mass. It is the point where the mass is balanced.
Which of the following is true for a rigid body?
A It deforms under load
B It has no deformation under load
C It is only used in fluid mechanics
D It cannot rotate
A rigid body is an idealized object that does not deform under load. It is used in mechanics to simplify the analysis of motion and equilibrium.
What is the formula for calculating the angular momentum?
A Mass × Velocity × Radius
B Force × Distance
C Mass × Acceleration
D Force / Area
Angular momentum (L) is the rotational equivalent of linear momentum. It is calculated as L = m × v × r, where m is mass, v is velocity, and r is the radius of rotation.
Which of the following is true for a simply supported beam?
A It is used only for vertical loads
B It has fixed supports at both ends
C It cannot carry bending moments
D It has a hinge support at one end and a roller at the other
A simply supported beam has a hinge support at one end and a roller support at the other. It allows rotation and horizontal movement at the supports.
What is the formula for calculating the strain energy?
A (1/2) × Stress × Strain × Volume
B Force × Distance
C Mass × Acceleration
D Force / Area
Strain energy is the energy stored in a material due to deformation. It is calculated as U = (1/2) × Stress × Strain × Volume.