1. Analyses of Bolted Joint for Bolt Preload and Shear Load
Two surface interface conditions:
1) Bonded contact surfaces between shim plate and flanges
2) Frictionless contact surface between shim plate and flanges
Two load cases:
Case 1: Shear load of 15 kip
Case 2: Combination of 60 kip bolt preload and 15 kip shear load.

2. FEA Model A286 stud Coupling Uz Coupling Ux, Uy, and Uz
INCO 718 washer
G-11CR washer
Flange stellalloy
316 SS shim w/ ins.break
A286 spherical washer set
G-11CR bushing
A286 hex nut
Coupling Ux, Uy, and Uz
Fixed support

3. Assumptions:
Except frictionless shim-flange contact surface, all compressive interfaces under preload are “glued” instead of bonded contacts in order to avoid the contact penetrations that affect the joint stiffness.
For stability, the G-11 bushings were glued to the flange stellalloy but have frictionless contact with the A286 stud.
The hex nuts are glued to the stud without any tolerance.
The spherical washer sets were modeled by equivalent short cylinders.
The thickness of shim was formed by 1/7 of G-11CR insulation and 6/7 of 316 SS. The equivalent smear material property was assumed.
The lower flange stellalloy was fixed at the bottom surface. The upper flange stellalloy was coupled in the vertical direction on the top surface nodal points.
Couples are applied at two side faces of the stellalloy to form a cyclically symmetric model.
The 60 kip pretension was applied about the mid-height of the stud and the15 kip shear load was applied normal to the side face of upper flange,
All analyses used the room temperature material propertied as shown on next slide.

4. Material Properties

5. Shear Load - Deformed Shapes with Undeformed Edge
▪ Bonded contact has much smaller displacement than the frictionless contact case
Bonded contact
Frictionless contact
Undeformed shape
Deformed shape
Scale factor = 60
Unit in inch

6. Combined Load - Deformed Shapes with Undeformed Edge
Frictionless contact
Bonded contact
Mainly due to bolt shorten for preload
Deformed shape
Scale factor = 60
Unit in inch

7. Shear Load - Deformed Shape with Undeformed Edge
Bonded contact
Frictionless contact
Undeformed shape
Deformed shape
Scale factor = 60 Uy
Usum
Usum Uy
Unit in inch

8. Combined Load - Deformed Shapes with Undeformed Edge
Bonded contact
Frictionless contact
Deformed shape
Scale factor = 60
Usum Uy
Usum Uy
Unit in inch

9. Shear Load - von Mises Stress in Flange Stellalloy
Bonded contact
Frictionless contact
high local stress at edge is the combination of the bearing stress and shear stress primarily in the y direction
Unit in psi

10. Combined Load - von Mises Stress in Flange Stellalloy
Frictionless contact
Bonded contact
high local stress located at the washer bearing surface primarily due to preload
Unit in psi

11. Shear Load - Stress in Stud, Nut, and Washer
Frictionless contact
Bonded contact
Deformed shape
Scale factor = 60 Sz
Seqv Sz
Seqv
Unit in psi

12. Combined Load - Stress in Stud
Bonded contact
Frictionless contact
Peak stresses occur at the faces of nuts due to the assumption that stud and nut are bonded
Deformed shape
Scale factor = 60 Sz
Seqv Sz
Seqv
Unit in psi

13. Shear Load - von Mises Stress in Bushing
Note: Bushings were glued to the flanges. If they are not glued, the deformed shape will be changed.
Frictionless contact
Bonded contact
Deformed shape
Scale factor = 60
Unit in psi

14. Combined Load - von Mises Stress in Bushing
Note: Bushing was glued to flange
Bonded contact
Frictionless contact
Deformed shape
Scale factor = 60
Unit in psi

15. Shear load - Contact Pressure on Bushing
Frictionless contact
Bonded contact
Deformed shape
Scale factor = 60
Unit in psi

16. Combined load - Contact Pressure on Bushing
Bonded contact
Frictionless contact
No contact pressure on bushing due to Poison’s effect of the preload on bolt and small shear displacement
Unit in psi
Deformed shape
Scale factor = 60

17. Discussions:
The analyses intend to observe the structural behaviors of bolt joint subjected to preload and shear force under the two extreme conditions of the friction between the shim plate and the flange stellalloy.
The bonded case has much smaller lateral displacement than the frictionless case.
With frictionless case, the lateral displacement is mostly contributed by the shear load. The lateral stiffness of the joint is dominated by the bending and shearing stiffness of the bolt as well as the contact pressure on the bushing.
In the bonded case, the majority of shear force transporting between flanges depend on the shear stiffness of shim plate while in frictionless case, they are transferred through bearing on the bushing and bolt hole. This shows the high friction coefficient and larger shim plate improve the joint rigidity.
Bonded case produced much smaller stress on all parts of the joint than the frictionless case, that means a much better joint design.
The bending stress on the bolt is about 2.0 ksi for 1.0 kip of shear force. Tight fit of the bolt will reduce the bending stress on the bolt.
Bearing stresses on the bushing are due to the bolt bending and the gap tolerance. The maximum bearing stress do not occurs at ends of bushings because the bolt bending was restrained by the nuts and washers.