Strength of Materials I EGCE201 กำลังวัสดุ 1

1. Strength of Materials I EGCE201กำลังวัสดุ 1 Instructor: ดร.วรรณสิริ พันธ์อุไร (อ.ปู) ห้องทำงาน:6391 ภาควิชาวิศวกรรมโยธา E-mail: egwpr@mahidol.ac.th โทรศัพท์: 66(0) 2889-2138ต่อ6391 www.egmu.net/~civil/wonsiri

2. Shearing Stress in Multiple Shafts Static equilibrium must be satisfied. The vector of all applied torques = 0 TA+TB+TC+TD=0 The shearing stress at any point in the shaft is a function of the Internal torque on a plane containing the point. The maximum Stress is computed from Internal torque Radius of the shaft The polar moment of inertia

3. The shearing stress at a point on shaft through which section 1 passescan only be defined once the internal torque is determined. From the free-body diagram,the internal torque at the section The shearing stress is given by

4. The shearing stress at a point on shaft through which section 2 passescan only be defined once the internal torque is determined. From the free-body diagram,the internal torque at the section The shearing stress is given by

5. Angle of Twist in Multiple Shafts • For this shaft sections AB, BC, and CE will each have different • Internal torque (FBD) • Polar moment of inertia • Shear Modulus • Length The angle of twist of the end of a shaft consisting of N sections is expressed as

7. Relative Rotation In some situations both ends of a shaft rotate. The angle of twist is the angle through which one end rotates w.r.t the other. fixed Both rotates Shaft AB

9. Shearing Stress on inclined planes

10. Shearing Stress on inclined planes

11. Statically Indeterminate Shafts • Both ends of the shaft are built in, leading to two reaction torques but one has only one moment equilibrium equation. • The compatibility equation is the relative rotation! • See example

12. Assuming a counterclockwise torque is positive, summing moments about the axis of the shaft results in The total angle of twist of the shaft must be 0 since both ends are fixed.

14. โจทย์ตัวอย่างทบทวนความเค้นเฉือนภายใต้ภาระบิดโจทย์ตัวอย่างทบทวนความเค้นเฉือนภายใต้ภาระบิด

15. 1.

16. 2.

18. 3.

19. 4.

20. 5.

21. 5. continued

22. 5. continued

23. 6.

24. 6. continued

25. 6. continued