Pj Problems - Overview
The Number Line
7 Spaces Of Interest - Overview
Triadic Unit Mesh
States Of Matter
COHN - Natures Engineering Of The Human Body
The Human-Body Systems
Faith, Love, Charity
Determine maximum flexure stress at section A-B of beam resting on simple supports as illustrated in figure 125.6(a).
S7P3A31 (Force - Pull).
Pj Problem of Interest is of type force (pull).
Flexure Stress (bending stress) can be tensile or compressive.
Tensile flexure stress: convex side of a bent beam
Compressive flexure stress: concave side of a bent beam.
Assumptions: Principles of consistent deformation and superposition are applicable. Elasticity holds.
Beam is relatively weightless and has a neutral axis (line of zero stress in a member subject to bending).
Simple supports are those not capable of exerting a moment on the beam.
Equations of Interest:
flexure stress, σf = (Mc)/I
M = moment applied to the section bearing stress of interest (lb in)
c = distance from the neutral axis of cross section to the outermost edges of the section (inches).
I = moment of inertia of the section about its neutral axis (in4).
Summation of moments about a point or section, ΣM = 0.
Sum of forces in any direction, ΣF = 0.
Moment of inertia for a rectangular section (figure 125.6(c)) = (zy3)/12
Clockwise moments are considered positive
Anti-clockwise moments are considered negative.
So, for moment about R1 (left simple support figure 125.6(a)):
ΣM1 = 0 = (P)(L/2) - (R2)(L)
Where L is distance between simple supports.
So, R2 = P/2.
Similarly, for moment about R2 (right simple support)
R1 = P/2.
Sum of vertical forces &Sima;Fy = 0
So, P - R1 - R2 = 0 (down positve, up negative).
figure 125.6 illustrates free body diagram of the beam to the right of section A-B.
Vertical shear load acts on section A-B.
So, summation of moments about A-B gives:
ΣMA-b = 0 = Px/2 - M.
So, M = Px/2.
Where M = moment needed in beam in order to maintain equilibrium of the free body
For a rectangular section:
I = (zy3)/12 (see figure 125.6(c))
c = y/2
So, flexure stress, σf = (Mc)/I = [(M)(y/2)]/(zy3)/12
The portion of beam to the right can also be used to calculate the moment M.
In this case, shear load P/2 in section acts upward
Moment M, in section is counterclockwise
Distance from section to right simple support is L-x
P is at play distance 1/2 from right support.
The point . is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.
Derivation Of The Area Of A Circle, A Sector Of A Circle And A Circular Ring
Derivation Of The Area Of A Trapezoid, A Rectangle And A Triangle
Derivation Of The Area Of An Ellipse
Derivation Of Volume Of A Cylinder
Derivation Of Volume Of A Sphere
Derivation Of Volume Of A Cone
Derivation Of Volume Of A Torus
Derivation Of Volume Of A Paraboloid
Volume Obtained By Revolving The Curve y = x2 About The X Axis
Single Variable Functions
Absolute Value Functions
Equation Of The Ascent Path Of An Airplane
Calculating Capacity Of A Video Adapter Board Memory
Probability Density Functions
Boolean Algebra - Logic Functions
Ordinary Differential Equations (ODEs)
Infinite Sequences And Series
Introduction To Group Theory
Advanced Calculus - Partial Derivatives
Advanced Calculus - General Charateristics Of Partial Differential Equations
Advanced Calculus - Jacobians
Advanced Calculus - Solving PDEs By The Method Of Separation Of Variables
Advanced Calculus - Fourier Series
Advanced Calculus - Multiple Integrals
Production Schedule That Maximizes Profit Given Constraint Equation
Separation Of Variables As Solution Method For Homogeneous Heat Flow Equation
Newton And Fourier Cooling Laws Applied To Heat Flow Boundary Conditions
Derivation Of Heat Equation For A One-Dimensional Heat Flow
The Universe is composed of matter and radiant energy. Matter is any kind of mass-energy that moves with velocities less than the velocity of light. Radiant energy is any kind of mass-energy that moves with the velocity of light.
Composition And Structure Of Matter
How Matter Gets Composed
How Matter Gets Composed (2)
Molecular Structure Of Matter
Molecular Shapes: Bond Length, Bond Angle
Molecular Shapes: Valence Shell Electron Pair Repulsion
Molecular Shapes: Orbital Hybridization
Molecular Shapes: Sigma Bonds Pi Bonds
Molecular Shapes: Non ABn Molecules
Molecular Orbital Theory
More Pj Problem Strings