ENGN2217 Flashcards

Amy Bryan
Flashcards by Amy Bryan, updated more than 1 year ago
Amy Bryan
Created by Amy Bryan almost 6 years ago


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External Loads A body is subjected to only 2 types of external loads. Surface forces and body forces.
Surface forces When two surfaces touch one another. Force evenly distributed and if area thin can be approximated by a linear distributed load.
Body Forces When one body exerts a force on another without them touching i.e. gravity. Normally represented by a single concentrated force. i.e center of gravity
Support reactions Only in the joints where restriction of movement occurs
Equilibrium sum of forces and moments must equal 0 Draw a FBD
Normal force, bending moment, shear force, torsional moment
Coplanar loadings Only have shear force, bending moment and normal force
Stress assumptions Material is continuous Material is cohesive (no cracks)
Stress unit Pa= 1N/m^2
State of stress A cubic section can be cut out of a member to give the state of stress shown below.
Stress directions Normal stress acts normal to the change in area Shear force acts tangential to the change in area
Prismatic All cross sectionals are the same
Homogeneous same physical and mechanical properties all the way through
Isotropic Same properties in all directions
Constant normal stress distribuion uniform stress distribution means there must be a constant normal stress distribution.
Average normal stress equation
Tension vs compression Note that stress is in equilibrium.
Maximum average normal stress Must analysis all sections where the cross sectional area or force changes for the largest P/A ratio. Use a axial/normal force force diagram.
Average shear stress equation
Shear stress equilibrium Shear stress mus be in equilibrium for pure shear to occur
Average shear special case In some case double shear may occur in which case the shear force v is divided by 2
Allowable stress equation Same equation can be used but instead of force normal stress or shear stress can be used.
Finding allowable stress
Deformation When a body changes in size or shape
Normal Strain The change in length of a line per unit length
Normal Strain equation
Shear Strain Change in angle caused by deformation
Shear strain equation
Cartesian Normal strain Equations represent the final lengths of the shape in the x,y and z co-ordinates
Cartesian Shear Strain The equations for the approximate angles between sides
Cartesian strain summary
Small strain analysis IF normal strains <<1
Strain changing by a function of x integrate the Cartesian normal strain over the length of the bar.
Strain tip USE TRIG!
Nominal/engineering stress
nominal/engineering strain
Stress/strain diagram
Elastic behavior Ranges up to the elastic limit. Up until this point the specimen returns to it's original shape once the load is removed.
Yielding Occurs after the yield stress. Permanent deformation occurs here. Specimen continues to elongate even without an increase in load.
Strain Hardening Occurs after yielding. Marks a point where more load can be handled by the specimen . This process will flatten off until in reaches the ultimate stress.
Ductile material Can be subjected to large strains before fracuring
Percent elongation formula
Percent reduction in area formula
Brittle materials Materials that have little to no yielding before failure.
Hooke's Law Equation represents the initial straight line of the stress strain curve
Elastic recovery Once a specimen has been deformed it can recover after unloading this represents a slope E on the stress strain diagram.
Strain energy Internal energy in a specimen when deformed by an external load
Modulus of Resilience Strain energy density when the stress reaches the proportional limit. i.e. area under the elastic region in a stress strain diagram.
Modulus of resilience equation
Modulus of toughness Area under the entire stress strain diagram. i.e. maximum amount of energy a material can absorb.
longitudinal and lateral strain Used to calculate Poisson's ratio
Poisson's Ratio Usually negative and different for every material
Shear modulus of elasticity Represents the slope of a t-y diagram
The shear stress strain diagram
Shear modulus/modulus of elasticity formula
Another strain defiition Can be thought ofas change in length over change in time. Therfore can intergrate to find the length
Saint-Venant’s principle Where after appoint the localised stress becomes the same as the average stress
Displacement in terms of x
Displacement for constant force, E and area
Displacement for segmented forces, areas or E's
Displacement sign convention
Principle of superposition When the stress or displacement of segments can be added together to compute the overall stress/dislacement for the member.
Condition for superposition 1. Load must be liearly related to the stress of displacement 2. Load must not significantly change the geometry or configuration of the member.
Compatibility condition equation that specifies conditions for displacement
Thermal displacement equation
Stress concentrations Complex stress distribuions can occur where the cross sectional area in a member changes.
Stress contcentraion factor equation
Stress concentration graphs Graphs can help to determine the stress concentration factor for many specimens
Torque Torque is a moment that twists a member around it's longatudinal axis
Torision: Shear stress vs max shear stress equation P is the radial position C is the outer radius
Torision: Max shear stress equation T is the internal torque c is the ouer radius J is the polar moment
Torsion: Shear stress equation
Polar moment: Solid shaft
Polar Moment: Tubular shaft
Power transmission The works per unit time required to rotate the shaft
Power transmission equation
Power Transmission Frequency formula This formula can be used or P=Tw Where w is the angular frequency
Shaft design formula Used to design the geometry of the specimen i.e. using J or c
Angle of twist The amount of rotation or twist that occurs in a secimen
Angle of twist in terms of x
Angle of twist for a consant cross section
Angle of twist for multiple torques
Sign convention Angle of twist Use the right hand rule
Note on summing angles of twist Only valid if shear stress does not exceed the proportional limit.
Torsion case: Two fixedsupports at either end of a member angle of twist must equal 0
Angle of twist case 2: two materials bound together Angles of twist must be equal to each other
Torsion: Stress concentrations The torsion formula can not be used when there is a sudden change in cross secional area. So K is used in this formula
Torsion: Stress concentration graphs Stress concentraton graphs can be used to calculate K
Example of different beam types
Shear and moment diagrams The shear force and bending moments graphed across a position x along a beam
Beam sign convention
Beam Long straight member loaded perpendicular to it's longatudinal axis
Complex loadings for determining V and M Relationships between the diagrams can be used todetermine the graphs shape.
More relationships
Bending a straight member: assumption 1 The longatudinal axis does not experience any change in length
Bending straight member: assumption 2 All cross sections remain plane and perpendicular to the longaudinal axis
Bending a straight member: assumption 3 And deformation in a cross sections plane will be ignored
Label of axis (straight member)
Strain for a deformed straight member
Define p and y variables
Relating stress to the maximum stress equation Y is the distance from the y axis c is the radius
Flexure formula: Maximum stress Where c is the radius
Flexure formula: At a point
Flexure formula condition Resultant internal moment is equal to moment produced by the stress distribuion about the normal axis.
Normal Stress at a point
Angle of moment at a single point a is the angle of the neutral axis theta is the angle of the moment
Stress concentrations: when you can't use the flexure formula
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