Engineering Statics

Shear and Bending Moment diagram for a beam with several concentrated loads.  Student can't see V & M diagrams a hints.

Classic problem of a vehicle parked on an incline.  Best solved by rotating the coordinate system.

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Find roots and the area under a parabola

Given a random spandrel, find the expressions for the differential elements of area and the coordinates of its centroid needed to determine the location of the centroid by integration. 

Find the centroid and the centroidal moments of inertia for a beam composed of a flat plate and two angle sections.

Calculate the centroidal moment of intertia of a rectangle with a excentric rectangular hole.

Calculate the moment of inertia of a composite shape consiting of two rectangles about the x or y-axis.  Parallel axis theorem is often required.

Sum three force vectors based on a written description of the situation.

Determine the mechanical advantage of a pair of compound lopping shears.

An A-frame structure supporting a force or a moment.  One leg is a two force body.

Find all forces on a two-part, symmetrical frame supporting a load. 

An A-frame structure supporting a force and a moment. The feet are at the same vertical position, so taking moments at one foot yields the y component of the reaction at the other.

Solve Truss by the method of joints.  The solution is simplified by recognizing symmetry.

Classic machine problem.  Find the mechanical advantage of a pair of pliers and the force on the hinge pin.

Find the centroidal moment of inertia of a sideways T shape. This requires first locating the centroid, then applying the parallel axis theorem.

Solve for the internal force in three members of a truss.

Find the rectangular (scalar) components of a force for two coordinates systems.

Friction

Student estimates, then calculates exactly and symbolically the value of $k$ for a parabola $y = k x^2$ which passes through a given point.

A hand truck on wheels.  Easiest to solve by rotating coordinate system.

Two forces act on a bell crank. This problem has two unknown magnitudes and an unknown direction which makes it tricky to solve by the equilibrium equation method.  

The solution is much simpler if three force body principle is used.

Find the reactions of a rigid body (a triangular plate) at a pin and roller, using the three-force body principle.

Two known forces, and a third with known magnitude act on a rigid body.  Apply $\Sigma M = 0$ about a pin restraint to determine the direction of the third force.  The problem has two valid answers.

Given three vectors, arrange them in a tip to tail arrangement using geogebra, then estimate the magnitude and direction of their resultant.

Add three vectors by determining their scalar components, summing them and then resolving the rectangular components to find the magnitude and direction of the resultant

Two dimensional particle equilibrium problem.  Advice shows how to use how to use slope triangles to find sines and cosines, rather than finding the angle and using that.