# ENGN2217 Flashcards

Flashcards by Amy Bryan, updated more than 1 year ago Created by Amy Bryan almost 6 years ago
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 Question Answer 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. Necking 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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