Answer :
Final answer:
A suitable rectangular cross section for the tension member would have a width of 3 inches and a height of 1.08 inches.
Explanation:
To select a rectangular cross section for the tension member, we need to calculate the required area of the member based on the applied loads. The total load on the member is the sum of the service dead load (DL) and the service live load (LL). In this case, DL is given as 25 kip and LL is given as 45 kip.
To convert the loads to pounds, we need to multiply them by 1000. Therefore, DL becomes 25,000 pounds and LL becomes 45,000 pounds.
The required area of the member can be calculated using the formula:
Area = Total Load / Allowable Stress
For A36 steel, the allowable stress is typically taken as 0.6 times the yield strength. The yield strength of A36 steel is approximately 36 ksi (kips per square inch).
Let's calculate the required area:
Area = (DL + LL) / (0.6 * Yield Strength)
Substituting the given values:
Area = (25,000 + 45,000) / (0.6 * 36,000)
Area = 70,000 / 21,600
Area ≈ 3.24 square inches
Now that we have the required area, we can choose a rectangular cross section that meets this requirement. The cross-sectional area of a rectangle is given by the formula:
Area = Width * Height
Since we are not given any constraints on the dimensions of the member, we can choose any width and height combination that satisfies the required area. For example, we can choose a width of 3 inches and a height of 1.08 inches:
Area = 3 * 1.08
Area ≈ 3.24 square inches
Therefore, a rectangular cross section with a width of 3 inches and a height of 1.08 inches would be suitable for the tension member.
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