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Analysis and design eccentric loading
- 1. 𝐹 𝐺 𝑥 𝑥 𝑦 𝑦 Analysis and Design of Eccentrically Loaded Members August 28, 2020 Vijay Kumar Professor and Dean Mechatronics Engineering Chitkara University
- 2. 2 Eccentric loads Effect of eccentric load State of stress Design equation The Flow…
- 4. Load acting parallel to the member axis Load acting perpendicular to the member axis Load acting in-plane of the member Shift the load to the CG of member geometry Find the effect of the load on the member Show the state of the stress at critical point Develop the design equation Analysis of Eccentrically Loaded Member
- 5. 𝐹𝑒 𝐶𝐵 𝐹 𝑀 = 𝐹𝑒 𝐶𝐵 𝐹 𝐹 𝐵 𝐹𝑒 𝐶 What would be the effect of load at a point along the axis of the load? What would be the effect of load at a point away from the axis of the load? 𝐹 and 𝑀 𝑀 in the plane of cross section 𝑀 in a plane perpendicular to the plane of cross section Twisting Bending Axial deformation Load Transfer and Effect of Load
- 6. Effect of forces and moments at point A Force along x-axis is transverse load and cause in-plane/transverse shear. Force along y-axis is also transverse load and cause in- plane/transverse shear. Force along z-axis is axial load and causes elongation. Couple ( 𝑀 𝑥−𝑦 ) in the plane of cross-section and hence induces twisting. Couple (𝑀 𝑦−𝑧) in the plane perpendicular to cross-section and hence causes bending in y-z plane. Couple (𝑀𝑧−𝑥) in the plane perpendicular to cross-section and hence causes bending in z-x plane. Member under General Loading
- 7. Net effect of all forces at point A 𝑭 𝒙 = 𝟒𝟎𝟎 N (+x) 𝑭 𝒚 = 𝟓𝟎𝟎 + 𝟑𝟎𝟎 + 𝟐𝟎𝟎 + 𝟗𝟎𝟎 = 𝟏𝟗𝟎𝟎 N (-y) 𝑭 𝒛 = 𝟔𝟎𝟎 N (+z) 𝑴 𝒙−𝒚 = −𝟑𝟐𝟎𝟎 + 𝟓𝟎𝟎𝟎 + 𝟏𝟓𝟎𝟎 = 𝟑𝟑𝟎𝟎 N-m, (cw) 𝑴 𝒚−𝒛 = −𝟏𝟎𝟎𝟎𝟎 + 𝟒𝟖𝟎𝟎 − 𝟔𝟎𝟎𝟎 − 𝟒𝟎𝟎𝟎 − 𝟗𝟎𝟎𝟎 = 𝟐𝟒𝟐𝟎𝟎 N-m (acw) 𝑴 𝒛−𝒙 = 𝟔𝟎𝟎𝟎 − 𝟖𝟎𝟎𝟎 = 𝟐𝟎𝟎𝟎 N-m (acw) Solution
- 8. Effect of Load and Corresponding Induced Stresses Elongation Tensile stressAxial tensile Load Compression Axial compressive Load Compressive/bearing stress Bending Moment acting in transverse plane Compressive and tensile stress Twisting Moment acting in plane of cross-section Torsional shear stress Sliding In-plane load In-plane shear stress 𝜎 = 𝐹 𝐴 𝜎 = 𝐹 𝐴 𝜎 = 𝐹𝑒 𝐼 𝑦 𝜏 = 𝐹 𝐴 𝜏 = 𝐹𝑒 𝐽 𝑟
- 9. 𝑀𝑡 𝑀𝑡 𝜏 𝜏 𝐹𝑥 𝐹𝑥 𝜎 𝑥 𝜎 𝑥 𝑀 𝑥𝑦 𝑀 𝑥𝑦 𝜎 𝑥 𝜎 𝑥 State of Stress 𝑀 𝑥𝑧 𝑀 𝑥𝑧
- 10. State of Stress : C-Clamp y 𝑡 𝒙 𝒚 𝒚 𝒙 𝑡 𝒙 𝒚 𝒚 𝒙
- 11. Neutral Axis y
- 12. State of Stress : Spindle of Hand Lever 𝜏 𝜎 𝜎 𝜏
- 13. 𝜎 𝜎 x y z State of Stress : Bolts
- 14. 𝜎𝜎 𝜏 𝜏 x y z State of Stress: Bolts
- 15. State of Stress: Bolts/Rivets 𝜏 𝜏
- 16. State of Stress: Weld 𝜏 𝜏
- 18. 𝜏 = 𝐹 𝐴 𝜎 = 𝐹𝑒 𝐼 𝑦𝜏 𝑝 = 𝐹 𝐴 𝜏 = 𝐹𝑒 𝐽 𝑟 𝜏 = 𝐹 𝐴 𝜎 = 𝐹 𝐴 𝜎 = 𝐹 𝐴 𝜎 = 𝐹𝑒 𝐼 𝑦 𝜏 = 𝐹 𝐴 𝜏 𝑠 = 𝐹𝑒 𝐽 𝑟 Bending BendingElongation Elongation In-plane Shear In-plane Shear Twisting Twisting In-plane Shear
- 19. 𝜏 = 𝐹 𝐴 𝜎 = 𝐹𝑒 𝐼 𝑦 𝜏 = 𝐹𝑒 𝐽 𝑟 𝜎 = 𝐹𝑒 𝐼 𝑦
- 20. 20 Thanks