STATICS

A body is called statically indeterminate when: 1. There are more unknown external reactions than there are available independent equilibrium equations. 2. The number of available independent equilibrium equations is more than the number of unknown external reactions. 3. The number of available independent equilibrium equations is equal to the number of unknown external reactions. 4. The laws of Statics do not apply to the object.

1

A direction cosine is: 1. The cosine of the angle between a vector and a particular coordinate axis. 2. A unit vector that points in the direction of a vector. 3. The cosine of the angle between a vector and the horizontal plane. 4. The magnitude of a vector

1

The center of mass and the center of gravity: 1. Coincide if the gravitational field is uniform and parallel for all parts of the object. 2. Always coincide. 3. Are never located at the same point on an object. 4. Coincide only if the object has uniform thickness.

1

The direction of a couple vector M: 1. Is always perpendicular to the plane of the forces which constitute the couple. 2. Is always parallel to the plane of the forces which constitute the couple. 3. Could be parallel to or perpendicular to the plane of the forces which constitute the couple. 4. Is always parallel to the direction of one of the forces which constitute the couple.

1

A multiforce member must have: 1. At least four forces acting on it. 2. Forces applied at three or more points, or forces applied at two or more points and at least one couple applied. 3. At least three applied forces and a couple acting on it. 4. At least one couple acting on it.

2

For a system of rectangular coordinates in two dimensions, for a force whose line of action is at an angle of θ, counterclockwise from the positive x axis, the x component of the force is given by: 1. Fx = F sinθ 2. Fx = F cosθ 3. Fx = F tanθ 4. Fx = F / cosθ

2

The representation in correct free-body diagram of the force of a flexible cable, belt, chain, or rope for which the weight of the cable, belt, chain, or rope is neglected is a: 1. Force in tension or compression along the cable, belt, chain, or rope and a force perpendicular to the cable, belt, chain, or rope. 2. Single force in tension along the cable, belt, chain, or rope. 3. Single force along the cable, belt, chain, or rope that is either in tension or compression. 4. Force in tension along the cable, belt, chain, or rope and a moment about which the cable, belt, chain, or rope is connected to an object.

2

The triple scalar product is used to calculate: 1. The scalar product of three vectors with each other. 2. The scalar magnitude of the moment of a force about an arbitrary axis. 3. The resultant force for a system of forces. 4. The scalar magnitude of a force.

2

Frames and machines differ from simple trusses in that: 1. Frames and machines are always larger than trusses. 2. Truss structures are always larger than frames and machines. 3. Trusses are composed only of two-force members whereas frames and machines have one or more multiforce member. 4. All frames and machines are statically indeterminate.

3

The necessary and sufficient conditions for three-dimensional equilibrium are: 1. ∑ Fx = 0 and ∑ Fy = 0, and the sum of the moments about an axis normal to the plane is zero. 2. ∑ Fx = 0 and ∑Fy = 0, ∑Fz = 0, and the sum of the moments about an axis normal to the plane is zero. 3. ∑ Fx = 0, ∑Fy = 0, and ∑Fz=0; ∑ Mx = 0, ∑My = 0, and ∑Mz= 0. 4. ∑Fx = 0 and ∑Fy = 0, ∑Fz = 0.

3

The projection or scalar component of a force along a line is found by: 1. Finding the direction cosines for the force with respect to a rectangular coordinate system. 2. Taking the cross product of the force and the unit vector representation of the line. 3. Taking the scalar product of the force and the unit vector representation of the line. 4. Finding the direction cosines for the line with respect to a rectangular coordinate system.

3

Triangles are the basic element in the design of simple trusses because: 1. They are more esthetically pleasing than other shapes. 2. They cost less to produce than other shapes, such as rectangles. 3. They provide rigidity that allows the truss to be treated as a rigid body. 4. They make the simple truss statically indeterminate.

3

For a statically determinate space truss with j joints, m members, and n external reactions, the relationship between the number of members m and the number of joints j and the numbers of external reactions n is: 1. 𝑚 + 𝑛/2 = 3𝑗. 2. 𝑚 + 2𝑛 = 3𝑗. 3. 2𝑚 + 𝑛 = 3𝑗. 4. 𝑚 + 𝑛 = 3𝑗.

4

If only two forces act on an object, and the object is in equilibrium, it must be the case that: 1. The forces must be equal in magnitude, and they must act in the same direction. 2. The magnitude of each of the forces is zero. 3. The forces must be equal in magnitude and they must be perpendicular to each other. 4. The forces must be equal in magnitude, opposite in direction and collinear.

4

In a free-body diagram for a fixed connection (embedded or welded) 3-D equilibrium it is necessary to show: 1. Only three mutually perpendicular forces. 2. Two mutually perpendicular forces and a couple about a single axis. 3. Only two mutually perpendicular forces. 4. Three mutually perpendicular forces and a couple acting along the axis of each of the forces.

4

The moment of a force describes: 1. The size or magnitude of a force. 2. The tendency of the force to move a body in the direction of its application. 3. The duration of application of the force. 4. The tendency of the force to tend to rotate a body about an axis.

4

The necessary and sufficient conditions for equilibrium of a general system of forces in a plane require: 1. ∑ Fx = 0 and ∑ Fy = 0. 2. ∑ Fx = 0 and ∑Fy = 0, and the sum of moments about either the x-axis or the y-axis is zero. 3. The sum of moments about an axis normal to the plane is zero. 4. ∑ Fx = 0 and ∑ Fy = 0 and the sum of moments about an axis normal to the plane is zero.

4

The positions of the centroid and the center of mass: 1. Coincide for all objects. 2. Are never the same on a given object. 3. Are the same for objects of non-uniform density. 4. Coincide only for objects of uniform density.

4

Beams are defined as structural members which: A) Offer resistance to bending when a load is applied. B) Are always supported at their ends. C) Do not deflect under loads. D) Cannot support a distributed load.

A

For r as a position vector which runs from the moment reference point to any point on the line of action of a force F the moment M of the force about the point may be calculated as: A) M = r × F . B) M = F × r . C) M = r · F . D) M = F / r .

A

If a rigid body has a ball-and-socket joint, the free-body diagram of the body will include the following at the joint: A) Only three mutually perpendicular forces. B) Two mutually perpendicular forces and a couple about a single axis. C) Three mutually perpendicular forces and a couple acting along a single axis. D) Only two mutually perpendicular forces

A

In a simple truss for equilibrium the forces are assumed to be: A) Applied at the ends of the member and are equal, opposite, and collinear. B) Distributed uniformly along the length of the member. C) Applied at the ends of the member and are equal, in the same direction, and collinear D) Applied at the ends of the member and are equal, opposite, and perpendicular to the length of the member.

A

A direction cosine is: A) The cosine of the angle between a vector and a moment arm that is used for calculating the cross product. B) The cosine of the angle between a vector and one of the three rectangular coordinate axes. C) The cosine of the angle used to calculate the scalar product of a vector. D) Always positive

B

Equilibrium of forces which lie in a plane and are concurrent at a point requires: A) ΣFx = 0, ΣFy = 0, and ΣMo = 0. B) ΣMo = 0 only. C) ΣFx = 0 and ΣFy = 0 only. D) ΣFx = 0 or ΣFy = 0 and ΣMo = 0

B

The center of mass of an object: A) Is always at the same point as the center of gravity. B) Generally coincides with the center of gravity for objects considered in engineering analysis if the gravitational field for all parts of the object is uniform and parallel. C) Depends upon the variation of the value and direction of the force of gravity for each part of the object. D) Must be located on the object

B

The proper representation of the force of a flexible cable, belt, chain, or rope if the weight of the cable, belt, chain, or rope is negligible is: A) A force along the cable, belt, chain, or rope either in tension or compression. B) A force along the cable, belt, chain, or rope in tension. C) A force with one component along the cable, belt, chain, or rope and another component perpendicular to the cable, belt, chain, or rope. D) A force in tension along the cable, belt, chain, or rope and a moment about the point at which the cable, belt, chain, or rope is connected to the object

B

Varignon's Theorem is useful for calculating the moment of a force about a point by: A) Using only scalar equations. B) Using the sum of the moments of the components of the force about the same point. C) Eliminating the need for using the moment arm in calculating the moment. D) Allowing the use of a moment arm of arbitrary length.

B

A multiforce member must have: A) At least three applied forces acting on it. B) At least three applied forces and a couple acting on it. C) Three or more applied forces, or two or more forces and one or more couple acting on it. D) At least four applied forces acting on it.

C

A rigid body is an object: A) That rigidly stays in one place because it is immovable under the action of any force. B) That provides a large resistance to any force that is used to try to move it. C) In which the change in distance between any two points on it is negligible when forces are applied to it. D) That cannot rotate when a force is applied to it

C

Frames and machines: A) Contain only two-force members. B) Contain multiforce members for which the forces are directed along the length of the member. C) Contain multiforce members for which the forces are generally not directed along the length of the member. D) Can be analyzed by the same techniques used to analyze trusses.

C

In analyzing the unknown forces acting on a given pin in a plane truss, obtaining a negative answer for the value of a force means: A) The truss is unstable. B) There was a mathematical error in the calculations. C) The direction that was chosen for the force was incorrect, and the correct direction of the force is opposite to the direction that was chosen in the analysis. D) The value of the force cannot be determined by the Method of Joints.

C

In the Method of Sections used in analyzing a plane truss: A) There is no limit to the number of unknowns that can be obtained from a single free body diagram. B) At most two unknowns can be obtained from a single free body diagram. C) It is possible to solve for a maximum of three unknowns from a single free body diagram. D) It is possible to solve for a maximum of four unknowns from a single free body diagram.

C

Newton's Third Law states that: A)A particle remains at rest or continues to move with a uniform velocity if there is no unbalanced force acting on it. B) The acceleration of a particle is proportional to the vector sum of forces acting on it, and is in the direction of this vector sum. C) The forces of action and reaction between interacting bodies are equal in magnitude, opposite in direction, and collinear. D) The velocity of a particle is proportional to the vector sum of forces acting on it, and is in the direction of this vector sum.

C

A beam is a structural member that can: A) Support only tension or compression. B) Support tension or compression and resist only bending. C) Support tension or compression and resist bending and shear but cannot resist torsion. D) Support tension or compression and resist bending, shear, and torsion.

D

The complete specification of the action of a force must include: A) The magnitude and direction of the force. B) The magnitude and point of application of the force. C) The direction and point of application of the force. D) The magnitude, direction, and point of application of the force

D

The necessary and sufficient conditions for three-dimensional equilibrium are: A) ΣFx = 0 and ΣFy = 0 and the sum of moments about an axis normal to the plane is zero. B) ΣFx = 0, ΣFy = 0, ΣFz = 0, and the sum of moments about an axis normal to the plane is zero. C) ΣFx = 0, ΣFy = 0, ΣFz = 0, ΣMx = 0, and ΣMy = 0. D) ΣFx = 0, ΣFy = 0, ΣFz = 0, ΣMx = 0, ΣMy = 0, and ΣMz = 0.

D

The necessary and sufficient requirement for equilibrium of an object that is subject to two-dimensional loading is: A) The summation of the forces in the x direction equals zero and the summation of forces in the y direction equals zero. B) The forces must be collinear. C) The summation of the moments about any point on or off the object is zero. D) The summation of the forces in the x direction equals zero, the summation of the forces in the y direction equals zero, and the summation of the moments about any point on or off the body is zero.

D

The positions of the centroid and the center of mass: A) Coincide for all objects. B) Are never the same on a given object. C) Are the same for objects of non-uniform density. D) Coincide only for objects of uniform density.

D

The resultant of a system of forces: A) Is any combination of forces that is equivalent to the original system of forces. B)Is the simplest force combination which can replace the original forces without altering the internal effect on the rigid body to which the original forces are applied. C) Is always equal to zero. D) Is the simplest force combination which can replace the original forces without altering the external effect on the rigid body to which the original forces are applied.

D

The term "couple" is used to describe: A) Any moment about a point. B) The moment produced by two forces which are perpendicular to each other. C) The moment produced by two forces that are equal, opposite, and act along the same line of action. D) The moment produced by two forces which are equal, opposite, and noncollinear.

D