CHAPTER 2 : STATIC LOADING

2.1 STRESS DISTRIBUTION IN BASIC MACHINE COMPONENTS

1. Rod

Critical point (in general): Any point Critical point (specifically): At stress

cncentrated points

2.1 STRESS DISTRIBUTION IN BASIC MACHINE COMPONENTS

Stress at stress concentrated points

2.1 STRESS DISTRIBUTION IN BASIC MACHINE COMPONENTS

Shear stress in a ‘rod’ (pin, bolt and rivet)

Shear stress (ave) = P/A

2.1 STRESS DISTRIBUTION IN BASIC MACHINE COMPONENTS

Bearing stress in a ‘rod’ (pin, bolt and rivet)

2.1 STRESS DISTRIBUTION IN BASIC MACHINE COMPONENTS

2. Beama. Normal stressb. Transverse shear stressc. Deflection

2.1 STRESS DISTRIBUTION IN BASIC MACHINE COMPONENTS

Normal stress: Along beam direction Maximum at the top or at the bottom

x

My

I

2.1 STRESS DISTRIBUTION IN BASIC MACHINE COMPONENTS

(for rectangular beam)

• Shear Stress

2.1 STRESS DISTRIBUTION IN BASIC MACHINE COMPONENTS

2.1 STRESS DISTRIBUTION IN BASIC MACHINE COMPONENTS

Critical points:

In beams actually, we design for normal stress and shear stress separately.

x x

xy

2.1 STRESS DISTRIBUTION IN BASIC MACHINE COMPONENTS

Deflection

Assuming linear in material and geometry,

P1

x

y

w dx

2

2

dx

ydEIM

2.1 STRESS DISTRIBUTION IN BASIC MACHINE COMPONENTS

Design of beams Prismatic design:

Design for normal stress

Sreqd = Required section modulus

For long beam. Design for shear stress

For short beam with concentrated loadEspecially for wood beam

Fully stressed beam design

2.1 STRESS DISTRIBUTION IN BASIC MACHINE COMPONENTS

T

L

GJ

TL

J

T

3. Shaft

2.1 STRESS DISTRIBUTION IN BASIC MACHINE COMPONENTS

4. Thin Cylinder

2.1 STRESS DISTRIBUTION IN BASIC MACHINE COMPONENTS

5. Thick Cylinder

P2

P1

R2

R1

2.1 STRESS DISTRIBUTION IN BASIC MACHINE COMPONENTS

Critical Points: Inner points: r = R1

Highest maximum shear stress

r

H

R

2.2 MATERIAL PROPERTIES Basic material properties:

Physical: Density Mechanical:

Young’s modulus Shear modulus Yield strength UTS Elongation at break Reduction of area Poisson’s ratio Toughness: modulus of toughness, modulus of resilience Hardness (Brinnel, Rockwell, Vickers) Impact strength (Izod, Charpy)

Test: Tensile test Hardness test Impact test

2.2 MATERIAL PROPERTIES

Tensile test

2.2 MATERIAL PROPERTIES

Standard codes 1. Society of Automotive Engineers (SAE) 2. British Standards (BS)3. European standards – (EN) 4. ASTM (UNS) 5. Japanese Industrial Standards (JIS) 6. Germany steel grades (DIN)7. China steel grades (GB)

2.2 MATERIAL PROPERTIES

Determine the alloy content, properties, applications and its code number.1. Cast Iron2. Carbon Steel & Alloys3. Stainless Steel & Alloys4. Aluminum & Alloys5. Magnesium & Alloys6. Copper &Alloys7. Titanium & Alloys8. Zircanium & Alloys9. Nickel & Alloys10. Zinc & Alloys

2.3 FAILURE THEORY

To develop FS of the design Static failure theory

Tresca’s theory von Misses’s theory

2.3 FAILURE THEORY

  1 1.25 - 1.5 for exceptionally reliable materials used under controllable conditions and subjected to loads and stresses that can be determined with certainty - used almost invariably where low weight is a particularly important consideration

  2 1.5 - 2 for well-known materials under reasonably constant environmental conditions, subjected to loads and stresses that can be determined readily.

  3 2 - 2.5 for average materials operated in ordinary environments and subjected to loads and stresses that can be determined.

  4 2.5 - 3 for less tried materials or for brittle materials under average conditions of environment, load and stress.

  5 3-4 for untried materials used under average conditions of environment, load and stress.

  6 3-4 should also be used with better-known materials that are to be used in uncertain environments or subject to uncertain stresses.

  7

 

Repeated loads : the factors established in items 1 to 6 are acceptable but must be applied to the endurance limit (ie. a fatigue strength ) rather than to the yield strength of the material.

  8

 

Impact forces : the factors given in items 3 to 6 are acceptable, but an impact factor (the above   dynamic magnification factor ) should be included.

  9

 

Brittle materials : where the ultimate strength is used as the theoretical maximum, the factors presented in items 1 to 6 should be approximately doubled.

10

 

Where higher factors might appear desirable, a more thorough analysis of the problem should be undertaken before deciding on their use.

based on yield strength - according to Juvinall & Marshek op cit.