Grade 10 Calculating Stress in a Square Bar

Grade 10 Calculating Stress in a Square Bar

Stress DIRECT STRESS Ø When a force is applied to an elastic body, the body deforms. The way in which the body deforms depends upon the type of force applied to it. Compression force makes the body shorter. A tensile force makes the body longer

Direct Forces Tensile and compressive forces are called DIRECT FORCES Stress is the force per unit area upon which it acts. …. . Unit is Pascal (Pa) or ( Simbol – Sigma) Note: Most of engineering fields used k. Pa, MPa, GPa.

Metric system of measurement • Before we are going to attempted any calculations, we must first get to know the different measurements in the metric system • They are: ü Decimal fraction of a meter ü SI Base units ü SI Derived units ü SI prefixes Mechanical Technology Curriculum Coordination & Support

Decimal Fraction Description of decimal fraction of 1 meter Name of unit , 001 one thousands of a meter millimetre , 01 one hundredth of a meter centimetre , 1 one tenth of a meter decimetre 1, 00 unit meter 1000 meters Kilometre Mechanical Technology Curriculum Coordination & Support

SI Base units Base Quantity Name Symbol Length meter m Mass Kilogram kg Time second s Mechanical Technology Curriculum Coordination & Support

SI Derived units Derived Quantity Name Symbol Area Metre square m² Volume Cubic metre m³ Speed, velocity Metre per second m/s Acceleration Metre per second squared m/s² Newton N Pascal Pa or N/m² Force Pressure, Stress Mechanical Technology Curriculum Coordination & Support

SI prefixes – NB!! Prefix Symbol Factor Multiple SI unit with Kilo k 10³ 1 000 Mega M 10⁶ 1 000 Giga G 10⁹ 1 000 000 Tera T 1012 1 000 000 Mechanical Technology Curriculum Coordination & Support

Calculations • Now that we understand the measurements of the metric system, we can now go and start doing the calculations. • The most important aspect of calculations, is the formula. If you UNDERSTAND the formula, you will have no problem solving the stress equations. Mechanical Technology Curriculum Coordination & Support

Understanding the formula • Let us see what the formula is all about: Stress. . . It is the internal force that act within the body of a material and it is measured in Pascal (Pa). Force. . . It is the load, mass or force that is acting on a body of a material and it is always measured in Newton (N) Note: Mass is kilogram and 1 kg = 10 N Mechanical Technology Curriculum Coordination & Support

Understanding the formula Load Stress = Area Units – Pascal (Pa) Units – Newton (N) Units – Metre squared (m²) Mechanical Technology Curriculum Coordination & Support

Understanding the formula • Area. . . This is the cross sectional area of the material. . . Cut the material in half and measure that area. In engineering we always measure in millimetres and NOTE that area measurement is in metre squared. . . so Mechanical Technology Curriculum Coordination & Support

Understanding the formula • The area for a square bar is. . . Length x Width • The area for a round bar is. . . Mechanical Technology Curriculum Coordination & Support

Understanding the formula • Because the units for area is in m², the following happens to the formulas: Square Bar Length x Width 10⁶ In order to take m² to mm², we have to divide by 10⁶ Round Bar NOTE: Mechanical Technology Curriculum Coordination & Support

Understanding the formula • Now to under stand why we use 10⁶. . . in a square metre this happens. . . 1 metre L 1 m x 1 m = 1 m² Now. . . 1 m = 1000 mm therefore 1000 mm x 1000 mm = 1 000 mm² or 10⁶ 1 metre W Mechanical Technology Curriculum Coordination & Support

Calculating Stress • Now that we fully understand the formula , we can go ahead and calculate the stress in a square bar or a round bar. Not that these two materials are solid materials and there are no holes in them. Mechanical Technology Curriculum Coordination & Support

Calculating Stress in a round bar • Example: Calculate the compressive stress in a 25 mm diameter round bar if it is subjected to a load of 12 k. N. Remember the formula: Mechanical Technology Curriculum Coordination & Support

Th ha e for ma ve to mula nip ula ted Note that we cannot calculate by using k. N – k = 1000 = 10³ Note that we cannot calculate a fraction within a fraction Mechanical Technology Curriculum Coordination & Support

Note that the comma has moved 6 spaces left. . . Threfore it is x 10⁶ or Mega = 244 462 992, 6506 Pa = 244, 46 MPa Mechanical Technology Curriculum Coordination & Support

Calculating Stress in a square bar • Example: Calculate the compressive stress in a 20 x 20 mm square bar if it is subjected to a load of 12 k. N. Remember the formula: The same calculating principals apply as in calculating a round bar Mechanical Technology Curriculum Coordination & Support

= 300 000 Pa = 300 MPa Mechanical Technology Curriculum Coordination & Support