Math Problem Statement

An engineering drawing marked with the dimensions used to machine the sample from a rectangular block of material. The length of the central portion of the sample is 50.00 mm having a width of 8.00 mm. A 45% ridge with a height of 1.50 mm at each end of the central portion extends the length of this section to 53.00 mm and the width to 11.0 mm. Each end of the sample has a threaded section of 15.00 mm. The width between the 50.00 mm central portion and the start of the threaded section is 10.00 mm.

Ridge detail: angled at 45 degrees to a point at the top and bottom of the sample, having a height of 1.50 mm and width of 2.91 mm. In Question 2a you are asked to calculate the stress acting on parts of a sample at the beginning and end of an experiment similar to that in Week 17. The load applied in the experiment was 4.51 kN.

All your answers to Question 2a should be given in appropriate units.

a.

i.To calculate the stress on the sample due to the applied tensile load you need to know the area over which this force is acting. Using information from Figure 2, calculate the relevant cross-sectional area of the sample within the gauge length at the start of the experiment in mm2 to 3 significant figures.

Solution

To calculate the stress acting on the sample, we first need to calculate the relevant cross-sectional area over which the tensile force is applied. Since the question focuses on the cross-sectional area within the gauge length, we'll use the dimensions provided for this region.

Dimensions Given:

  • Length of the central portion: 50.00 mm
  • Width of the central portion (gauge length): 8.00 mm
  • Ridge height at each end of the central portion: 1.50 mm
  • Total width including ridges: 11.00 mm
  • Ridge angle detail: 45 degrees

We'll start by calculating the cross-sectional area of the sample within the gauge length, which is the region of interest.

  1. Width of the sample at the gauge length: 8.00 mm
  2. Ridge height: 1.50 mm

Cross-sectional area calculation:

  • The cross-sectional area in the gauge length section will be the width times the thickness (which is unspecified in the problem but usually consistent across the sample).

Since no specific thickness of the sample is provided, I will assume the thickness remains constant across the sample. Let me know if you'd like me to assume a value for thickness or if it is provided elsewhere in your context.

Let me know how you'd like to proceed!

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Math Problem Analysis

Mathematical Concepts

Engineering Mechanics
Stress Calculation
Cross-sectional Area

Formulas

Stress = Force / Area
Cross-sectional Area = Width * Thickness

Theorems

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Suitable Grade Level

Undergraduate Engineering