Understanding Bolted Joints: Basics & Forces Explained

[havsula]

Hello
I really struggle with understand how and why bolted jonts actually works:
The following figure copied from http://ocw.mit.edu/courses/mechanic...pring-2009/lecture-notes/MIT2_72s09_lec10.pdf shows a bolted joint:

After the bolt is preloaded we have as system where k_m1 and k_m2 are in compression and k_b are streched.

The theory I have founds states that when an externcal force of F is applied to this system, some of the force is taken by the bolt F_b and some of the force are taken by the joints F_a
F = F_b + F_a

But I do not understand how the joints can take up load when they are not connected together. In my head only the bolt can take up force. What do I not understand?

 

[SteamKing]

A bolt is essentially a clamp which can be adjusted by turning the nut. While the shank of the bolt is in tension, the pieces being clamped together are in compression. The washers in the figure above, located under the head of the bolt and under the nut, help to spread out the clamping force, reducing the chance that any permanent set will be placed in the pieces being clamped.

http://en.wikipedia.org/wiki/Bolted_joint

 

[havsula]

A bolt is essentially a clamp which can be adjusted by turning the nut. While the shank of the bolt is in tension, the pieces being clamped together are in compression. The washers in the figure above, located under the head of the bolt and under the nut, help to spread out the clamping force, reducing the chance that any permanent set will be placed in the pieces being clamped.

http://en.wikipedia.org/wiki/Bolted_joint

Hello
But what I do not understand is how the stiffness of the clamps will add to the stiffness of the system
These forces pulls in each direction, the green lines is in some way the where the force will act in my head. There are no physical connection between the clamps so I cannot see that they add anything to the total stiffness. In my head the bolt carry all the load.

 

[MarkJW]

Highly recommended:

An Introduction to the Design and Behavior of Bolted Joints (Mechanical Engineering, Volume 97) Hardcover – July 19, 1995
by https://www.amazon.com/s/ref=dp_byline_sr_book_1?ie=UTF8&field-author=John+Bickford&search-alias=books&text=John+Bickford&sort=relevancerank&tag=pfamazon01-20 (Author)

https://www.amazon.com/dp/0824792971/?tag=pfamazon01-20

 

[MarkJW]

Hello
But what I do not understand is how the stiffness of the clamps will add to the stiffness of the system
These forces pulls in each direction, the green lines is in some way the where the force will act in my head. There are no physical connection between the clamps so I cannot see that they add anything to the total stiffness. In my head the bolt carry all the load.

View attachment 83813

In most cases, the bolt only adds a small amount of stiffness to the joint (maybe 5-15% depending on the plate stiffnesses). Think of preload as a load bank account. As the joint (plates and bolt together) start to separate, you are withdrawing some (pre)load from the bank account, and the plates dominate the stiffness of the joint. Once preload is exceeded on the applied force, then you are in trouble, because the bolt now carries the total preload plus the applied load, and your "bank account" is empty (i.e., the plates do not help you any more).

 

[Q_Goest]

Consider the bolt as a spring, just like it shows in your figure. It has some spring rate just like a spring does. The increase in length that occurs when you pull on the ends is linearly proportional to the tensile force.

Similarly, the parts clamping between the head and nut also act as springs, albeit much stiffer ones. They're in compression. The decrease in thickness of those parts is linearly proportional to the compressive force.

So when you take a spring (bolt) and pull it to stretch it, then hook it to a couple of much stiffer springs which go under compression, the bolt (light spring in tension) remains fairly well stretched while the members being clamped (heavy springs in compression) are compressed only slightly.

Do you know how to calculate the overall spring rate of the system as you've shown in the OP? Consider how to calculate the overall spring rate of that system of 3 springs (one bolt and two members being clamped). Can you write the equation for three springs as shown in that picture?

Now consider that when the system of 3 springs is pulled apart, you're actually pulling on the overall system of springs, not just the bolt. The ends of the springs (bolt and clamped members) move together, not independently. So when you move the ends of the bolt, you're pulling on the bolt but you're also reducing the compressive stress in the clamped members. What you're doing is actually pulling on 3 springs that are acting as one spring that has an overall spring rate that is much higher than either the bolts or the clamped members.

See if you can derive the equation for 3 springs as shown in the OP and then determine how forces acting on that set of 3 springs changes the overall length compared to how the same force would change the length of the bolt alone.

 

[havsula]

Consider the bolt as a spring, just like it shows in your figure. It has some spring rate just like a spring does. The increase in length that occurs when you pull on the ends is linearly proportional to the tensile force.

Similarly, the parts clamping between the head and nut also act as springs, albeit much stiffer ones. They're in compression. The decrease in thickness of those parts is linearly proportional to the compressive force.

So when you take a spring (bolt) and pull it to stretch it, then hook it to a couple of much stiffer springs which go under compression, the bolt (light spring in tension) remains fairly well stretched while the members being clamped (heavy springs in compression) are compressed only slightly.

Do you know how to calculate the overall spring rate of the system as you've shown in the OP? Consider how to calculate the overall spring rate of that system of 3 springs (one bolt and two members being clamped). Can you write the equation for three springs as shown in that picture?

Now consider that when the system of 3 springs is pulled apart, you're actually pulling on the overall system of springs, not just the bolt. The ends of the springs (bolt and clamped members) move together, not independently. So when you move the ends of the bolt, you're pulling on the bolt but you're also reducing the compressive stress in the clamped members. What you're doing is actually pulling on 3 springs that are acting as one spring that has an overall spring rate that is much higher than either the bolts or the clamped members.

See if you can derive the equation for 3 springs as shown in the OP and then determine how forces acting on that set of 3 springs changes the overall length compared to how the same force would change the length of the bolt alone.

I can put up the equations for the three springs if I have assumed that they are the part of the same system. But in order to try to explain:
As I can see the system it looks like that. Only the bolt have a physical connection between the upper and lower part of this system. So how can the joints add to the total stiffness of the system. When I apply a force, as far as I can see, all the tension will go in the bolt, which is physical connected to the upper part.

 

[Q_Goest]

Hi havsula,

After the bolt is preloaded we have as system where k_m1 and k_m2 are in compression and k_b are streched.

The theory I have founds states that when an externcal force of F is applied to this system, some of the force is taken by the bolt F_b and some of the force are taken by the joints F_a
F = F_b + F_a

But I do not understand how the joints can take up load when they are not connected together. In my head only the bolt can take up force. What do I not understand?

I think it's the part in bold above that you're having a conceptual issue with. The statement made is fairly commonly used when talking about bolted joints. It means that the joint is under compression and that compressive load diminishes when the parts are in tension. It does NOT mean that the joint goes into tension. All the tension is still in the bolt after the force is applied. All they are saying is that the compressive load on the joint diminishes to a greater degree than the tensile load in the bolt increases. That's a very important thing to understand because bolts are not good at resisting alternating stresses because of fatigue. They will tend to crack at the thread root, so the alternating stresses in bolts have to be minimized and a well designed bolted joint accomplishes that by providing a very high spring constant in the joint when compared to the bolt.