HW5+Solutions

# HW5+Solutions - HOMEWORK PROBLEMS Week 5 Due Friday 14...

This preview shows pages 1–3. Sign up to view the full content.

HOMEWORK PROBLEMS Week 5: Due Friday 14 October 1. Figure 1 shows an assembly for measuring the tensile strength of the wooden specimen AB . The specimen has thickness (perpendicular to the figure) of 10 mm and width d = 15 mm. If the wood fails in tension at a stress of 800 kPa, determine the force F at which the specimen will fail. If the wood also fails in shear (parallel to the grain) at a stress of 200 kPa, determine the minimum dimension h if shear failure is not to occur before tension failure. h d F F A B Figure 1 Solution h d F A B F Figure 1.1 Figure 1.1 shows a free-body diagram of the specimen cut in the middle, where the cross- sectional area is A = 10 × 15 = 150 mm 2 . The force F is perpendicular to the cut, so there will be a tensile stress σ = F A = F 150 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
and if F is in N, this will be in N/mm 2 = N/m 2 × 10 6 in other words, MPa. Since tensile failure occurs at 800 kPa, we conclude that F at failure is given by F 150 = 0 . 8 or F = 120 N . h F F/ 2 F/ 2 Figure 1.2 Figure 1.2 shows a free-body diagram of the specimen split along two lines parallel with the bar, leaving two small rectangles of wood behind in the left hand grip as shown. In this case, there are two cut surfaces, each of area h × 10 and they will share the load equally, giving a shear stress τ = F/ 2 h × 10 = F 20 h .
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern