DESIGN ASPECT – Loading Condition

Static loading – load is applied gradually and remains applied throughout part’s life.

Repeated loading – applied and removed several times (repetitive) during life. Fail by fatigue at stress lower than yield strength. Higher design factor is needed.

Impact – require large design factor. (i) sudden load causes stresses much higher than computed. (ii) require part to absorb energy of the impact.

Static loading but at high T – consider creep, microstructural changes, oxidation & corrosion & influence of method of fabrication on creep.

Designing For Static Strength

Static strength Ability to resist short-term steady load at moderate T. Measured in terms as yield strength, UTS, compressive strength & hardness.

Aimed at avoiding yielding of the component and / or fracture.Component must be strong enough to support the load & may require stiffness to ensure deflections do not exceed certain limits.

Stiffness , important to avoid misalignment and maintain dimensional accuracy.

Elasticity (Young’s M) important when designing struts, columns & thin-walled cylinders subjected to compressive axial loading where failure can take place by buckling.

Component and structure made from ductile material are usually designed, so that no yield take place under static loading conditionBut, when the component is subjected to uniaxial stress, yielding take place

When local stress reaches the yield strength of the materialCritical cross-sectional area, A ;

A = KtnsL

YSKt = stress concentration factor

L = applied load

ns = factor of safety

YS = yield strength

Designing for simple axial loading

Factor of safety, ns.Is applied in designing component to ensure it will satisfactory perform its intended functionTo get the strength of material at allowable stress.

The definition, strength of material depends on the type of material and loading condition The factor of safety, ns.

ns = S / Sa

S = Nominal strength, Sa = Allowable strength / Design strength

It is important to define which type of service condition will the material work on before calculating the ns.i. Normal working conditionii. Limit working condition

Designing for simple axial loading

Brittle material such as gray cast iron do not exhibit yielding, so design based on ultimate strength.

General - % of elongation in a 2-in gage length is less than 5%

Brittle. e.g Al – except for castings, all is ductile.

Ductile material – large plastic deformation, so unfit for intended use. Design based on yield strength.

Design stress guidelines :

Ductile material, δd = Sy / 2

Brittle material, δd = UTS / 6

Designing for Static Strength

Given – (1) Magnitude & type of loading & (2) material condition.

Determine yield & ultimate strength & % elongation of material. Decide ductile or brittle.

Specify design factor (factor of safety).

Compute design stress.

Write equation for expected max stress. For direct normal stress, δmax = F/A

Set δmax = δd & solve for required cross-sectional area.

Determine minimum required dimension.

Determine Dimensions & Shape of Component

Soalan :

Satu struktur penyokong mesin akan dibebankan dengan beban

tegangan statik 16kN. Dicadangkan, dihasilkan dalam bentuk rod

empat segi daripada keluli gelek panas, AISI 1020. Berikan

dimensi yang sesuai untuk keratan rentas rod tersebut.

Analisis :

Objektif – tentu dimensi keratan rentas rod.

Diberi – F = 16 kN = 16 000 N beban statik.

Bahan – AISI 1020 HR, Sy = 331 MPa, 36% elongation

Contoh

Jawapan :

Analisis – Biar δ = δd = Sy / 2 bahan mulur.

Analisis tegasan – δ = F/A, maka A diperlukan

A = F / δd

Tetapi A = a2 (a = dimensi sisi square)

Dimensi minimum yang dibenarkan a = A

Maka Tegasan, δd = Sy/2 = 331 MPa/2

= 165.5 MPa (N/mm2)

Keratan rentas, A = F/ δd = (16 000 N) = 96.7mm2

(165.5 N/mm2)

Dimensi minimum a = A = 96.7 mm2 = 9.83 mm.

Dimensi minimum a = 10 mm.

Torsional – loading of a component / part that tends to cause it to rotate or twist.When torque is applied, shearing stress is developed & torsional deformation occurs, resulting in an angle of twist of one end of part relative to the other.Material must have sufficient rigidity for the part to perform properly in service.Torque = T = F x d where F = applied force & d = distance from action of force to axis of the part.Power = torque x rotational speed (n in rad/s).

Torsional shear stress, ζmax = Td / 2Ip where T = applied torque, d = diameter & Ip = polar moment of inertia of the cross section.

Designing for Torsional Loading

Designing for Torsional Loading

Critical cross sectional area can be calculated,

for circular shaft, 2Ip = KtnsT

d ζmax

where Kt = stress concentration factor

ns = factor of safety

Moment, Ip = πd4 / 32 for solid circular shaft &

Ip = π(d04 – di

4) / 32 for hollow circular shaft of inner di & outer d0.

ASTME code of practice ; allowable value of shear stress of 0.3 yield or 0.18 UTS.

For ductile material, design shear stress = yield / 2N (steady torsion, N = 2, so ζd = yield / 4)

Designing for Torsional LoadingTorsional rigidity of component is usually measured by the angle of twist, θ, per unit length. For circular shaft, θ is given by,

θ = T / GIp where G = modulus of elasticity in shear.

G = E / (2(1 + ν)) where ν = Poisson’s ratio.

Usual practice is limit the angular deflection in shafts to about 1 degree, i.e π/180 rad, in length of 20 times the diameter.

Stiffness of part differ depending on shape of the cross-section – circular section has higher rigidity compared to other structural shapes, i.e I-beams,wide-flange beams

Designing for Bending

Beam – component that carries load transversely, that is, perpendicular to its long axis.

Loading – normal concentrated load, inclined concentrated load, uniformly distributed load, varying distributed load & concentrated moments.

Moment – an action that tends to cause rotation of an object. Can be produced by a pair of parallel forces acting in opposite directions, called couple.

Beam types ; simple, overhanging, cantilever, compound & continuous.

Bending moments – internal moments cause bending.

Designing for Bending

Overhanging – bend downward, negative bending

Load

MCantilever – one fixed end, provide support & moment produced by load

F

F

Compound – two or more parts extending in different directions.

Continuous – extra support or both ends fixed, require different approaches to analyze forces & moments.

Designing for Bending

Relation between bending moment, max allowable stress & dimensions given by ;

Z = nsM

YS where Z = section modulus = I/c

c = distance from center of gravity of cross section to the outermost fiber/beam.

I = moment of inertia of cross section with respect to neutral axis normal to direction of load.

M = bending moment & YS = max allowable stress.

ns = factor of safety.

Designing for Bending

Designing for Bending

When load is placed on a beam, the beam is bent and every portion of it is moved in a direction parallel to the direction of the load.

The distance that a point on the beam moves/ deflection depends

i. Its position in the beam

ii. Type of beam

iii. Type of support

Example

Question :

Determine the diameter of a cantilever beam of length 1 m

and rectangular cross section of depth-to-width ratio 2:1.

The cantilever is expected not to deflect more than 50 mm

for every 1000 N increment of load at its tip. The material

used in making the beam is steel AISI 4340 with a yield

strength of 1420 MPa and UTS 1800 MPa. What is the max

permissible load ? Assume a suitable factor of safety.

Example

Solution :The deflection ( y ) is given by relationship :

y = ( Ll3 ) / ( 3 EI )

where l = the length of cantilever

E = elastic modulus of the cantilever material

= 210 Gpa

I = the second moment of area of the cross-section

From fig 4.3

I = b x ( 2b )3 = 1000 x 1 x 1000 12 50 x 3 x 210 x 109

Where b is the width of the beam; b = 14.77 mm

Taking a factor of safety n = 1.5 and using eq.

Z = 2148 mm3 = ( nM ) / YS = ( 1.5 x L x l ) / 1420

The safe value of L = 2033 N

Example