Statics

Question 1

Explain the conditions for a rigid body to be in static equilibrium.

Answer 1

A rigid body is in static equilibrium when the vector sum of all external forces acting on it is zero in each direction, and the vector sum of all external moments (torques) about any point is also zero.

Question 2

Describe how the equations of equilibrium (sum of forces and sum of moments) apply to a structure.

Answer 2

The equations of equilibrium, namely the sum of forces and the sum of moments being equal to zero, provide a mathematical foundation for analyzing a structure’s static equilibrium by ensuring that external forces are balanced and external torques are counteracted, allowing for the determination of unknown forces and reactions within the structure.

Question 3

Explain how to determine support reactions for statically determinate structures.

Answer 3

To determine support reactions for statically determinate structures, apply the equations of equilibrium (sum of forces and sum of moments) to isolate and solve for the unknown support reactions by considering the constraints and external loads acting on the structure.

Question 4

Define and explain internal forces such as axial force, shear force, and bending moment.

Answer 4

Internal forces in a structural element include axial force, which represents tension or compression along the element’s axis; shear force, indicating lateral force parallel to the element’s cross-section; and bending moment, signifying the rotational effect caused by forces perpendicular to the element, causing flexural deformation.

Question 5

Discuss the relationship between external loads and internal forces in a structure

Answer 5

The relationship between external loads and internal forces in a structure is governed by equilibrium principles, wherein external loads induce internal forces such as axial forces, shear forces, and bending moments, ensuring that the structure remains in static equilibrium with balanced internal reactions to external actions.

Question 6

Discuss the concept of friction and its effects on equilibrium.

Answer 6

Friction is a resisting force that opposes the relative motion or tendency of motion between two surfaces in contact; its effects on equilibrium involve introducing additional forces in reaction to applied loads, influencing support reactions and potentially affecting the stability and balance of a structure

Question 7

Explain the difference between the equilibrium of particles and the equilibrium of rigid bodies.

Answer 7

The equilibrium of particles is concerned with the balance of forces acting on a single point, ensuring the sum of forces is zero; whereas the equilibrium of rigid bodies involves the balance of both forces and moments acting on an extended object, with the sum of forces and sum of moments equalling zero to maintain a state of static equilibrium.

Question 8

Define the moment of inertia and explain its significance in structural analysis.

Answer 8

The moment of inertia is a measure of an object’s resistance to changes in its rotational motion, calculated as the sum of each mass element multiplied by the square of its distance from the axis of rotation; in structural analysis, it is significant for evaluating a member’s ability to resist bending and its influence on the distribution of internal forces in beams.

Question 9

Location of Centroid

Answer 9

Set up table fo area, location of x or y from desired axis, and then multiply these values

Question 10

Gradient (square) Force

Answer 10

Moment: wx d x d/2
Fy or Fx: w x d

Question 11

Triangular Force

Answer 11

Moment: 1/2 w x d x d/3
Fx: 1/2w x d

Question 12

Method of Joints:

Answer 12

1. Find reaction @ supports
2. Select a joint that does not have more than 2 unknowns
3. Draw FBD of joint

Question 13

Tension =

Answer 13

Forces going AWAY from joint

Question 14

Compression =

Answer 14

Forces going TOWARDS joint