Final answer:
The question involves calculating the vertical displacement of a 500-lb load supported by four stainless steel wires. By applying Hooke's law and knowing the material properties of 304 stainless steel, the elongation due to the load can be determined.
Step-by-step explanation:
The student is asking about the vertical displacement of a 500-lb load supported by four 304 stainless steel wires when the load is applied. Given that each wire has a cross-sectional area of 0.025 inches squared and the members were originally horizontal, we must first calculate the tension in each wire due to the load. Assuming the load is evenly distributed, each wire supports 125 lbs or the equivalent in force units, which is approximately 556.5 Newtons (since 1 lb is approximately 4.44822 Newtons).
Next, we would use Hooke's law for the elongation of the wires, which states that the elongation (ΔL) is directly proportional to the force (F) applied, the length of the wire (L), and inversely proportional to the cross-sectional area (A) and the modulus of elasticity (E) of the material. The formula is ΔL = FL / (AE). To find E for 304 stainless steel, we can look it up in a reference table since it is a material property. The modulus of elasticity for 304 stainless steel is typically about 193 GPa, or 193 x 10^9 N/m². With the area in square meters and the force in Newtons, we would be able to calculate the elongation and therefore the vertical displacement of the load.