Bending Flashcards
Define Beams
Members that have loads applied perpendicular to the longitudinal axis
What are Internal forces
reaction forces that oppose the motion of the beam as a result of a load
ie. if you stretch the beam, the internal force will provide unequal but opposite force
What is a sagging beam
Beam with positive bending moment
looks like a smile
What is a hogging beam
Beam with negative bending moment
looks like a frown
Define Positive shear force
Clockwise Shear Force
(Left side has a force Upwards, internal side has a force Downwards)
Define Negative shear force
clockwise Shear Force
(Right side has a force Upwards, Left side has a force Downwards)
Will the Following Beam produce a Positive Shear Force at Point A , or a negative Shear force?
Explain Why?
Positive Shear Force
Point Force is trying to push beam down
Hence a Shear force is going to be in a direction to oppose this motion.
hence positive shear force
Draw the Bending Moment and Shear Force diagram for the Following Beam
Draw the Bending Moment and Shear Force diagram for the Following Beam
Draw the Bending Moment and Shear Force diagram for the Following Beam
Draw the Bending Moment and Shear Force diagram for the Following Beam
Which of the Following Shear Force Diagrams is correct?
E
Beam is Hogging, internal forces want to pull the beam clockwise , hence positive shear force
Point Load , the shear force of every cross-section will equal the point load, not dependant on distance
Which of the Following Shear Force Diagrams is correct?
C
Beam is Hogging, internal forces want to pull the beam clockwise , hence positive shear force
Distributed load, the total shear force of the cross sections is directly proportional to the distance
Maximum Shear Force at support of beam , Q = W(L-x)
Which of the Following Bending Moment Diagrams is correct?
D
Beam is Hogging, Hence Negative Bending Moment
Point Load , Bending moment as you go towards the point load will decrease, as there is less distance between the cross-section and the point load.
Which of the Following Bending Moment Diagrams is correct?
A
Beam is Hogging, Hence Negative Bending Moment
Distributed load,Maximum Shear Force at support of beam , Q = W(L-x) , hence Maximum bending moment is at the same point
What is Bending moment?
How much an object bending / moving at that specific point.
Higher the magnitude, higher the chance of breaking there
Draw the Bending Moment and Shear Force diagram for the Following Beam
Draw the Bending Moment and Shear Force diagram for the Following Beam
using superposition find the Shear Force Diagram
using super position find the bending moment diagram
What is the bending moment at a Pin/Roller Support
0 unless there is an externally applied moment at the support
Has to be 0 , as the support doesn’t move
Explain the Concept of a Neutral Surface
When a Beam is Bent, some of the atoms are compressed and some are stretched
A Beam is composed of an infibate amount surfaces (cross sections)
Some of these Surfaces are Compressed and some are Stretched
Compressed surfaces have -ve strain , Tensile surfaces have +ve Strain
So observing these surfaces, as you go from negative strain to positive, there must be a surface that experiences 0 strain and zero stress. - called a neutral surface
What is a Neutral Axis
The Intersection of the Neutral Surface and the cross-section of the beam
What are the 4 Assumptions in calculating the Deformation of a Beam
- Cross Section of a Straight Beam Remains plane when a beam deforms due to bending
( take two points on opposite sides of the beam, before bending they are reflections of one-another in the neutral axis , after bending this still must be the case) - The Neutral Surface and Neutral Axis is subjected to zero Normal Stress
- Longitudinal Strain Varies lineraly from Zero at the Neutral Axis to the maximum at the outer fibres of the beam
- Material is Homogenous and Elastic for the whole duration of bending
Hence we assume
Stress = Elastic Constant * Strain
Derive how do you calculate the stress of at a point of a beam subject to bending deformation
Derive the formula to calculate the internal force of a point of distance y from the neutral axis
Derive the formula to calculate the internal moment of a point of distance y from the neutral axis
Derive the formula to calculate the position of the neutral axis
Derive how
Calculate the Position of the Neutral Axis of the Following Shape.
Calculate the Position of the Neutral Axis of the Following Shape.
Using a rectangle derive the formula for the parallel axis theorem.
Using the Parallel Axis Theorem work out the second moment of area of the following shape .
What is the maximum stress acting on the beam made of the following cross section , if it is bent with a bending moment of 2000 kNM
what does the second moment of area tell us about a shape
It’s a measure of a shape’s ability to resist bending or flexure when subjected to a load. The greater the second moment of area, the more resistance the shape has to bending.
Using the Parallel Axis Theorem work out the second moment of area of the following shape .
A Beam with the following cross section is subject to a bending moment of 12kNM
Calculate the direct stress along the top surface of the hollow area and the bottom surface along the hollow area.
The maximum Direct Stresses
And Plot a Direct STress Distribution
the following I-Beam carries a bending moment of 2000 kNM calculate the maximum stress at the top and bottom of the Flange/ Web Joints
