Statics and Mechanics

83 flashcards by MentisLibrary

Free body diagrams, moments, trusses, stress and strain, and beam bending, the core toolkit every mechanical engineer reaches for first. Each card pairs the governing equation with a worked example.

What is the difference between a scalar and a vector quantity?
A scalar has magnitude only, such as mass, temperature or work. A vector has magnitude and direction and must be added by the parallelogram law, such as force, moment or velocity.
How do you resolve a force into rectangular components in two dimensions?
Project the force onto the x and y axes using the angle it makes with the positive x axis.
What does the dot product tell you in statics?
It returns a scalar equal to the projection of one vector onto another, which gives both the component of a force along a line and the angle between two vectors.
What does the cross product produce, and why does order matter?
It produces a vector perpendicular to both inputs, with magnitude AB sin(theta). It is used for moments. Reversing the order flips the sign.
What must appear on a correct free body diagram?
One body isolated from everything touching it, showing every external force and couple that acts on it: applied loads, support reactions, and weight, plus dimensions and a coordinate system.
Where does the weight of a body act on a free body diagram?
At the center of gravity, directed vertically downward, regardless of how the body is oriented or supported.
What is a two-force member and why is it so useful?
A member loaded at only two points with no couples applied. Equilibrium forces the two forces to be equal, opposite and collinear along the line joining the two points.
How is the moment of a force about a point defined?
As the force magnitude times the perpendicular distance from the point to the line of action of the force. It measures the tendency of the force to rotate the body about that point.
State the principle of moments (Varignon's theorem).
The moment of a force about a point equals the sum of the moments of its components about the same point.
What is a couple, and what makes it different from a single force?
Two equal, opposite, parallel forces that are not collinear. Their resultant force is zero, so a couple produces pure rotation with no tendency to translate the body.
How do you move a force to a different point without changing its effect on a rigid body?
Apply the force at the new point and add a couple equal to the moment of the original force about that new point. This is an equivalent force-couple system.
What are the three scalar equilibrium equations for a rigid body in two dimensions?
Two force sums and one moment sum must all be zero.
What makes a structure statically indeterminate?
It has more unknown reactions or member forces than there are independent equilibrium equations, so statics alone cannot find them. Compatibility of deformation must be added.
What reactions does a pin (hinge) support supply in a planar problem?
Two force components, usually taken as horizontal and vertical. It prevents translation in both directions but allows rotation, so it supplies no couple.
What reaction does a roller support supply?
A single force perpendicular to the surface the roller bears on. It allows both rotation and motion along the surface.
What reactions does a fixed (built-in) support supply in two dimensions?
Two force components and a couple, because it prevents horizontal translation, vertical translation and rotation.
What assumptions define an ideal truss?
Straight members joined by frictionless pins, loads and reactions applied only at the joints, and member weights neglected or lumped at the joints.
How does the method of joints work?
Isolate each pin as a particle, then apply the two force equilibrium equations at that joint. Start at a joint with no more than two unknown member forces and work through the truss.
How does the method of sections work?
Cut an imaginary line completely through the truss, keep one side as a free body, and apply the three rigid body equilibrium equations to the exposed member forces.
How do you recognize a zero-force member in a truss?
At an unloaded joint with only two noncollinear members, both are zero. At an unloaded joint with three members where two are collinear, the third is zero.
How do you check whether a planar truss is statically determinate?
Compare the number of members plus reactions with twice the number of joints, since each joint supplies two equations.
How do you tell tension from compression when solving a truss?
Assume every unknown member force pulls away from the joint, that is, assume tension. A positive answer confirms tension and a negative answer means the member is in compression.
How do frames and machines differ from trusses?
They contain at least one multi-force member, so members carry bending and shear as well as axial force. Frames are stationary structures; machines contain moving parts and transmit or modify forces.
What is the standard procedure for analyzing a frame?
If the frame holds together as a rigid unit, find the external reactions first, then dismember it and draw a free body diagram of each member, applying equilibrium to each.
Why must pin forces be drawn equal and opposite on two connected members?
Because of Newton's third law: the force member A exerts on the pin equals and opposes the force the pin exerts on member A.
How do you locate the centroid of a composite area?
Split it into simple shapes, take the first moment of each area about a reference axis, sum, and divide by the total area.
Where is the centroid of a triangular area?
One third of the height above the base, on the median from the apex to the midpoint of the base.
What does the second moment of area (area moment of inertia) actually measure?
How the area is distributed away from an axis. It is the geometric measure of a cross section's resistance to bending.
What is the moment of inertia of a rectangle about its centroidal axis?
One twelfth of the width times the depth cubed, with the depth measured in the bending direction.
What are the moments of inertia of a solid circular section?
About any diameter it is pi d^4 / 64, and the polar moment about the center is pi d^4 / 32.