10a-Bending_Stresses_in_Beams

.pdf

School

University of British Columbia *

*We aren’t endorsed by this school

Course

276

Subject

Mechanical Engineering

Date

Oct 30, 2023

Type

pdf

Pages

24

Uploaded by CommodoreIronGoat8

1 Mechanics of Wood Products Topic 10a: Bending Stresses in Beams
Introduction 2 The system of internal forces (axial, shear, and moment) which may exist at a section of a beam will cause internal stresses on that section: Axial forces N(x) will cause normal stresses Moments M(x) will also cause normal stresses Shear forces V(x) will cause shear stresses A N = σ ? = σ = ? τ
Introduction 3 Take the case where a beam is under pure bending, i.e., N(x)=V(x)=0, a segment of the beam will be in equilibrium under the action of the internal moment alone. Here, we want to study how to determine the internal stress distribution arising from the application of a bending moment M at any section of a beam. M M
Introduction 4 Basic Assumptions: The moment at a section is assumed to be delivered statically without shock or impact. The beam is assumed to be stable under the applied moment; i.e., no lateral buckling. The beam is assumed straight and prismatic (constant cross sectional area) with at least one axis of symmetry. X-sectional view
Curvature 5 As a member under bending will deform into a curve shape, let us first introduce the concept of curvature. Consider a curve in the x-y plane as shown. And let us examine an infinitesimal element ds of the curve. x y a b o ds φ+ φ d d d φ φ φ ρ ρ c
Curvature 6 at point 'a', the slope or tangent of the curve is φ . at point 'b', the slope of the curve is φ+ d φ . From geometry, aob=d φ where the point 'o' is the intersection point of the normals to curve at points 'a' and 'b' since points 'a' and 'b' are close together; i.e., ds is small, we have oa=ob= ρ . => ρ d φ = ds
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help

Browse Popular Homework Q&A

Q: heel in 93 par d) ... ) Construct the 95% confidence interval for the percentage of all auto…
Q: [Review Topics] [References] Use the References to access important values if needed for this…
Q: Only about 18% of all people can wiggle their ears. Is this percent different for millionaires? Of…
Q: Find the values of x for which the series converges. (If the answer is an interval, enter your…
Q: major research study concluded that the mean number of times that adolescents had engaged in…
Q: Find the buoyant force of a rectangular solid of the given dimensions submerged in water so that the…
Q: 5. Triangle ABC has vertices A(-3, 1), B(0, 3), and C(3, 0) and is dilated by a factor of using the…
Q: Use enthalpies of formation to calculate the standard enthalpy of reaction for the following…
Q: groups exists difference
Q: By rewriting the formula for the Multiplication Rule, you can write a formula for finding…
Q: What type of monosaccharide derivative is shown here?
Q: A person pushes horizontally with constant force P on a 260 N box resting on a frictionless…
Q: When muscle is at rest, creatine phosphate is produced from ATP in order to store energy. What is…
Q: 14. Researchers discover that New Mexican whiptails mated with a different species of lizard several…
Q: What is the decay probability per second per nucleus of a substance with a half-life of 22.5 hours?
Q: In the figure, the 200-lb crate is being pulled up the slope by the motor M. If the velocity of the…
Q: K A stem-and-leaf plot for the number of touchdowns scored by all Division 1A football teams is…
Q: (x) = cos x − 8x , [0, 4π] Find all relative extrema of the function. Use the Second Derivative Test…
Q: A ball thrown horizontally from the top of a building hits the ground in 0.400 s. If it had been…
Q: For the following concentration cell, use the Nernst equation to determine the expected voltage.…
Q: Calculate the accrued interest in dollars, and the total purchase price and dollars of the bond…
Q: Business calculus