Load & Stress Analysis
Load & Stress AnalysisDeliverables for the LectureMaterial
Strength & Stiffness (Stress-Strain Relations)Equilibrium &
Free Body DiagramsMohr CircleShear Forces & Bending
MomentsTorsionStress ConcentrationMaterial Strength &
StiffnessTensile Tests are used to determine the variety of
material strengths and characteristicsMaterials original dimensions
are recorded and then mounted on a Tensile Testing Machine and
slowly loadedLoad (P) is converted to stress by calculation
Material Strength & StiffnessThe results are then plotted as
a stress strain diagram (opposite)As seen ductile materials deform
much more than brittle ones
Ductile Material
Brittle MaterialMaterial Strength & Stiffnesspl Proportional
limit The point when the curve first starts to deviate from
proportionality limit (100% recovery if the load is removed) Hookes
law holdsStress = Youngs Modulus (E) X StrainYoungs Modulus (E),
measure of strength of material ( slope of stress-stain graph)
Ductile Material
Brittle MaterialplMaterial Strength & Stiffnessel Elastic
limit Beyond it plastic deformation would beginThough
proportionality no longer exists in stress strain curve, but still
100% recovery would be achieved
Ductile Material
Brittle MaterialelMaterial Strength & Stiffnessy Yield Point
Strain increases Rapidly without much increase in stressSince not
very pronounced, so yield Strength Sy is calculated by offset
method i.e. slope of line ay. Point a is predefined usually 0.2% of
original gauge length l0.
Ductile Material
Brittle MaterialyMaterial Strength & Stiffnessut ultimate
strength Maximum point on stress strain curveBeyond this point the
material exhibits a downward trend (due to necking) before
fracturing
Ductile Material
Brittle MaterialutMaterial Strength & Stiffnessf fracture
point At this point the material breaks
Ductile Material
Brittle MaterialfEngineering Stresses and True StressesValues
quoted in the diagram before corresponded to engineering stresses
as they considered the original gauge area of the specimenTrue
stresses are generally more than engineering stresses due to
neckingCross sectional Area must be measured simultaneously during
testing
Ductile Material True Stress Strain DiagramCompression &
Torsional TestsCompression tests are similar to tensile tests,
though a bit difficult due to problems in distributing the stresses
evenlyTorsional Tests are conducted by twisted solid cylindrical
bars and noting torque and twist angles.Similar notations as
tensile tests are used in torsion and compression testsCompression
and Tensile strengths are generally same for
materialsEquilibriumCondition for the equillibrium include Sum of
all forces =0 F = 0Sum of all moments =0 , M=0Two kinds of
equilibrium Static EquilibriumDynamic EquilibriumMost of the
designed parts are designed for equilibrium stateFree Body
DiagramsA complex analysis could be simplified by taking each
element, isolating it and analyzing it.Treating all members in this
manner would lead to yielding information regarding the total
system.This approach helps in establishing a logical way to
approach a complex problem Free Body DiagramDraw Free Body diagrams
for the system shown in opposite
Shear Force & Bending MomentsAnalytical Tools with
structural analysis to help perform structural design by
determining shear forces and bending moments at a given point.Helps
determine the type, size, material for a given set of loads for a
member for it to function without failureShear Force & Bending
MomentsShear forces & bending moments are both positive and
negative.Shear force tend to rotate an element CW +iveBM
compressing upper part but elongating lower +ive
Shear Force & Bending MomentsIn order to determine the Shear
Forces & Bending Moments Calculate the Reaction ForcesBreak the
member in segments (logically)Determine the Shear Forces & BM
of each segmentShear Force & Bending MomentsDetermine the BM
and SF at at x = (L/2)_x = (L/2)+
Shear Force & Bending MomentsCalculate the Reaction Forces
by applying equilibrium conditions
Shear Force & Bending MomentsSolve at x = (L/2)_
Shear Force & Bending MomentsSolve at x = (L/2)+
Mohrs CircleRepresentation to help determine the principle and
Max Shear stresses through their graphical representation
Construction of Mohrs Circle has already been taught to you.It
wont be addressed again Mohrs CirclePlot Mohrs Circle with x = 80
MPa and xy = 50 MPa cwMohrs CirclePlot Mohrs Circle with x = 80 MPa
and xy = 50 MPa cw
Stress ConcentrationIr-regular geometries (hole, bolt, weld) are
known as stress concentrators.Stress concentrators are areas which
magnify the stresses in the part
Stress Concentration Factor
Concentrators cause high stresses in structureA ratio (stress
concentration factor) of the max. stress to the nominal stress is
hence of interest for the designer
Stress Concentration FactorFactors affecting the stress
concentration factor include the size of the irregularity depth
(a), width (b) and radius of curvature ()Hence for a sharp crack
the stress concentrators may get to infinity
