A steady tensile load of 5.00kN is applied to a square bar, 12mm on a side and having a length of 1.65m. compute the stress in the bar and the resulting design factor if it is made from: (a) AISI 120 hot-rolled steel (b) AISI 8650 OQT 1000 steel, (c) ductile iron A536-84 (60-40-18) (d) aluminum allot 6061-T6 (e) titanium alloy Ti-6Al-4V annealed (f) rigid PVC plastic and (g) pheonolic plastic

To compute the stress in the bar, we can use the following formula:

Stress (σ) = Force (F) / Area (A)

Where: - Stress (σ) is in pascals (Pa) or megapascals (MPa) - Force (F) is in newtons (N) - Area (A) is the cross-sectional area in square meters (m²)

For a square bar, the cross-sectional area can be calculated by squaring the side length.

Firstly, we need to convert the given force from kilonewtons (kN) to newtons (N) and the dimensions from millimeters (mm) to meters (m): 5.00 kN = 5000 N 12 mm = 0.012 m

Now, calculate the cross-sectional area of the bar (A): A = side length × side length = 0.012 m × 0.012 m = 0.000144 m²

The stress in the bar is then: σ = F / A = 5000 N / 0.000144 m² = 34,722,222 Pa or 34.72 MPa

Next, for the resulting design factor, also known as the safety factor (n), it can be computed with the ultimate tensile strength (UTS) or yield strength of each material, depending on the context, and the applied stress:

Design factor (n) = UTS or Yield Strength / Stress

Provided we have the UTS or yield strength values for each of the materials, we would compute the design factor for each as follows:

a) AISI 120 hot-rolled steel: Let's say its UTS is UTS_steel_120. Then the design factor would be:

n_steel_120 = UTS_steil_120 / 34.72 MPa

b) AISI 8650 OQT 1000 steel: If its UTS is UTS_steel_8650, then:

n_steel_8650 = UTS_steel_8650 / 34.72 MPa

c) Ductile iron A536-84 (60-40-18): If its UTS is UTS_iron_A536, then:

n_iron_A536 = UTS_iron_A536 / 34.72 MPa

d) Aluminum alloy 6061-T6: If its UTS is UTS_aluminum_6061, then:

n_aluminum_6061 = UTS_aluminum_6061 / 34.72 MPa

e) Titanium alloy Ti-6Al-4V annealed: If its UTS is UTS_ti_6Al_4V, then:

n_ti_6Al_4V = UTS_ti_6Al_4V / 34.72 MPa

f) Rigid PVC plastic: If its UTS is UTS_PVC, then:

n_PVC = UTS_PVC / 34.72 MPa

g) Phenolic plastic: If its UTS is UTS_phenolic, then:

n_phenolic = UTS_phenolic / 34.72 MPa

For actual values, refer to the material datasheets or standards for the ultimate tensile strength (UTS) or yield strength (YS) values.

Extra: Understanding stress in materials is fundamental in engineering and physics. Stress is the internal forces that particles of a material exert on each other. It is typically caused by external forces or loads acting on the material. Stress has units of pressure, which is force per unit area.

The design factor or safety factor is used in engineering design to provide a margin of safety. It is a ratio that takes into account unknowns, variability in material strengths, and unexpected loads or imperfections in the material. Using a higher design factor implies a more conservative design, which is typically used in areas where failure would have serious consequences.

Materials all have unique properties such as ultimate tensile strength (UTS), which is the maximum stress that the material can withstand while being stretched or pulled before necking, which is a reduction in area. Yield strength, on the other hand, is the stress at which a material begins to deform plastically. Once it is passed, the material is permanently deformed and does not return to its original shape.

Materials like steel, aluminum, titanium, and plastics each have different mechanical properties and therefore are selected for different applications based on their performance characteristics, such as strength to weight ratio, cost, machinability, corrosion resistance, and thermal properties.