Moment Diagram by Parts

The moment-area method of finding the deflection of a beam will demand the accurate computation of the area of a moment diagram, as well as the moment of such area about any axis. To pave its way, this section will deal on how to draw moment diagram by parts and to calculate the moment of such diagrams about a specified axis.
 

Basic Principles

  1. The bending moment caused by all forces to the left or to the right of any section is equal to the respective algebraic sum of the bending moments at that section caused by each load acting separately.
     
    $M = ( \, \Sigma M \, )_L = ( \, \Sigma M \, )_R$

     

  2. The moment of a load about a specified axis is always defined by the equation of a spandrel
     
    $y = kx^n$

    where n is the degree of power of x.

 

Solution to Problem 506 | Flexure Formula Jhun Vert Tue, 04/21/2020 - 11:20 pm

Problem 506
A flat steel bar, 1 inch wide by ¼ inch thick and 40 inches long, is bent by couples applied at the ends so that the midpoint deflection is 1.0 inch. Compute the stress in the bar and the magnitude of the couples. Use E = 29 × 106 psi.
 

Solution to Problem 332 | Flanged bolt couplings Jhun Vert Tue, 04/21/2020 - 01:53 pm

Problem 332
In a rivet group subjected to a twisting couple T, show that the torsion formula τ = Tρ/J can be used to find the shearing stress τ at the center of any rivet. Let J = ΣAρ2, where A is the area of a rivet at the radial distance ρ from the centroid of the rivet group.
 

Problem 527 and Problem 528 | Friction Jhun Vert Sun, 04/19/2020 - 09:29 pm

Problem 527
A homogeneous cylinder 3 m in diameter and weighing 30 kN is resting on two inclined planes as shown in Fig. P-527. If the angle of friction is 15° for all contact surfaces, compute the magnitude of the couple required to start the cylinder rotating counterclockwise.
 

Cylinder resting on the corner of two inclined planes