Eccentric Load, bolted joint, welded joint, riveted joint, other members

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…

3. Eccentrically Loaded Member

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

17. 𝐹𝑒
𝑥
𝑦
𝑧
𝑧 𝑧
𝑦
𝑦
𝐺
𝐹
𝐹𝑒
𝑙
𝜏
𝜎
𝐹
𝑏
1
2

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