Engineering Mechanics Problems

The x-coordinate of the centroid of an area, calculated as the first moment of the area about the y-axis divided by the total area

The y-coordinate of the centroid of an area. Calculated as the first moment of the area about the x-axis divided by the total area

The x and y coordinates that locate the geometric center of a 2D object or region.

The product of an area element and its distance from a reference axis.

x = (1/Area) * integral(x dA over the area).

The internal force that resists the tendency of a beam to slide or shear at a cross-section.

The centroid coordinates for a particular area defined by a curve.

The internal moment created within a beam when external forces cause it to bend.

The given equation is y = kx^(1/3), which forms a curved boundary.

A technique used to determine internal forces (shear and moment) in a structural member by analyzing a section.

Values are x= 2.99 in; y = 6.74 in.

A beam where the reactions at supports cannot be determined directly using the equilibrium equations of statics alone.

The centroid is dependent on area, moments about the x and y axes (Ax and Ay).

Finding shear and moment at a specific point on a beam.

The single force that represents the effect of a triangular distributed load on a beam. Calculated as half the base times the height of the triangle.

A method to analyze internal forces (like shear) in beams by cutting through the beam and analyzing the forces on one section.

Vertical forces acting on a beam at its support points to keep it from collapsing vertically. Sum of these forces must balance the total load on the beam.

The force acting internally within a beam that resists the tendency of the part of the beam to shear off from the rest.

The points where a beam is held stable and prevents rotation. Often represented by reactions.

The upward force at support A of a beam, exerted to counterbalance the downward force from the distributed load and the point load.

The upward force at support B of a beam, exerted to counterbalance the downward force from the distributed load and the point load.

A load that is spread along a beam. In this case, the load increases linearly from point A to point B.

Finding the vertical reaction forces at the supports (RA and RB) involves using the equations of equilibrium (sum of forces in vertical direction = 0, sum of moments about a point = 0).

To calculate the total distributed load on a beam you integrate the load distribution function along the length of the beam.

A load that acts uniformly over a length of a beam or structure, spread evenly.

The internal force that resists the tendency of a beam to slide or shear along its cross-section.

The internal force that resists the tendency of a beam to bend or rotate due to applied loads.

Shear force changes linearly with the distributed load. It decreases by the amount of the distributed load per unit length.

The internal force resisting the tendency of the beam to slide along the cut section at x = 6 ft. Calculated as -450 lb.

The internal moment causing the beam to bend at x = 6 ft. Calculated as -3000 lb-ft.

A state where the sum of all forces and moments acting on a body is zero. The body is either held at rest or moving at a constant velocity.

A diagram showing all the forces and moments acting on a body, isolated from its surroundings. Essential to analyze the forces and moments in equilibrium.

External forces that a support provides to a beam, preventing it from sliding or collapsing. Calculated in the equilibrium equations. The beam reactions in this example are RA and RB.