Intro Page 1 BACKGROUND This calculation doesn't provide the number of bolts, but usually, many small bol The follow-up step is to tighten these bolts as much as possible, for fear that t While there are a number of more subtle joint design issues, this very basic desi Most textbooks apply the safety factor to the bolt strength, while most practicio Simply stated, this is because a safety factor of 1.2 satisfies nobody, while the There are two basic situations to be considered in evaluating the behavior of the BOLTED JOINT BEHAVIOR When a bolt is tightened, its grip is stretched by the bolt preload force (Fi). compressed by this same preload force (Fi). When an external load (P) is later a the second Figure. As the applied load is increased, the joint clamping force wi will separate or unseat. Beyond the unseating load, the bolt tension (Fb) is equ joint in compression) is the basic method used to evaluate bolted joints. The fi to provide a simple graphical basis for understanding. From this graph, it shoul to choose the bolt preload that roughly matches the bolt strength to joint unseat opening statement, ...that the needed bolt section area (At) is roughly the joint The somewhat curious note is that bolts are often preloaded to 60-90% of proof st applied to the joint ...without overloading the bolt ! as the force divided by resulting deflection. The bolt is a cylinder that experi constant (Kb) is simply the elastic modulus (Eb) times the tensile stress area (A distribution of stresss and strains in the joint is both very non-uniform, and a practice is to define an '"equivalent spring region" around each bolt. as illustr small ends are meant to represent the head and nut areas, while the conical shape the middle of the joint. A simple approximation for the spring constant of this very lengthy analysis, this should be considered a reasonable approximation that equal (assuming the joint doesn't unseat). This means that the ratio of spring f spring constants. GENERAL COMMENTS The most basic design calculation for bolted joints is to divide the joint load ( to obtain the needed bolt cross section area (At). And, of course, a design safety factor m * When tightening the bolt, the force (Fb) stretching the bolt must be equal t * When loads are applied to the joint, the length changes in the bolt (Db) and combined forces: bolt (Fb), joint (Fm), and applied (P) must balance as illustrated by the top Figure. At the same time, this load (P) decreases the not there, which is illustrated by the dashed and solid lines in the top Figure. The important "joint stiffness fraction" (C) is obtained from the parallel spring model. The "joint stiffness fraction" (C) is obtained from the parallel spring model. The joint an
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Intro
Page 1
BACKGROUND
This calculation doesn't provide the number of bolts, but usually, many small bolts are better than a few large bolts.
The follow-up step is to tighten these bolts as much as possible, for fear that they might come loose in service.
While there are a number of more subtle joint design issues, this very basic design approach is surprizingly good !
Most textbooks apply the safety factor to the bolt strength, while most practicioners prefer the safety factor on joint loads.
Simply stated, this is because a safety factor of 1.2 satisfies nobody, while the safety factor of 4 means bolts may come loose.
There are two basic situations to be considered in evaluating the behavior of the bolted joint:
BOLTED JOINT BEHAVIOR
When a bolt is tightened, its grip is stretched by the bolt preload force (Fi). At the same time, the joint (or members) are
compressed by this same preload force (Fi). When an external load (P) is later applied to the joint, the bolt stretches more,
the second Figure. As the applied load is increased, the joint clamping force will approach zero, where upon the joint halves
will separate or unseat. Beyond the unseating load, the bolt tension (Fb) is equal to the joint load (P) ...as if the joint were
joint in compression) is the basic method used to evaluate bolted joints. The first two Figures are combined in the third,
to provide a simple graphical basis for understanding. From this graph, it should be apparent that the designer would like
to choose the bolt preload that roughly matches the bolt strength to joint unseating load. This is the justification for the
opening statement, ...that the needed bolt section area (At) is roughly the joint load (P) divided by the proof stress (Sp).
The somewhat curious note is that bolts are often preloaded to 60-90% of proof strength, and then a similar load can be
applied to the joint ...without overloading the bolt !
as the force divided by resulting deflection. The bolt is a cylinder that experiences uniform stretch, which means the spring
constant (Kb) is simply the elastic modulus (Eb) times the tensile stress area (At) divided by the grip length (L). The
distribution of stresss and strains in the joint is both very non-uniform, and a subject for lengthy analysis. The common
practice is to define an '"equivalent spring region" around each bolt. as illustrated by the cones in the second Figure. The
small ends are meant to represent the head and nut areas, while the conical shapes reflect the spreading of stresses in
the middle of the joint. A simple approximation for the spring constant of this volume is provided on the right. To avoid
very lengthy analysis, this should be considered a reasonable approximation that is neither precise, or highly repeatible.
equal (assuming the joint doesn't unseat). This means that the ratio of spring force changes is the same as the ratio of
spring constants.
GENERAL COMMENTS
The factors to be considered (failure modes, or limiting cases) in the selection of the bolt preload are:
1. Tensile yielding or failure in the bolt grip material.
The most basic design calculation for bolted joints is to divide the joint load (Pmax) by the bolt proof stress (Sp
to obtain the needed bolt cross section area (At). And, of course, a design safety factor must also be included !
* When tightening the bolt, the force (Fb) stretching the bolt must be equal to the force compressing the joint (F
* When loads are applied to the joint, the length changes in the bolt (Db) and joint (Dm) must be equal. Also, the
combined forces: bolt (Fb), joint (Fm), and applied (P) must balance (S F = 0).
as illustrated by the top Figure. At the same time, this load (P) decreases the joint (or member) compression, illustrated by
not there, which is illustrated by the dashed and solid lines in the top Figure. This parallel spring model (bolt in tension, and
The important "joint stiffness fraction" (C) is obtained from the parallel spring model. A spring constant (K) is defined
The "joint stiffness fraction" (C) is obtained from the parallel spring model. The joint and member spring deflections must be
Intro
Page 2
2. Compressive yielding (crush) of the joint material under the bolt head or nut.
3. Unseating (or seperation) of the joint halves.
4. Shear failure (or strippiing) of the threads at the thread major diameter.
So, for example, if the bolts are loose, the allowable joint loads would be limited by premature joint unseating
At first glance, it would appear that the desired preload is the value that would maximize the allowed joint load is the case
that would produce simultaneous failures by all four modes above. However, this approach tends to be modified when the
consequences of each of the failure modes are considered. The first two modes tend to be somewhat "forgiving", while the
last two tend to be more serious concerns. With ductile materials, a small amount of yielding will stretch the bolt or crush the
joint, which often has the net effect of relaxing the preload (Fi) to the value that should have been selected. However this also
reduces the service safety factors. If these chosen safety factors were generous, the results may still be acceptable.
Joint unseating tends to be more catistrophic because even small side loads will cause abrasive wear of the joint asperities
which very quickly reduces the bolt preload to zero (loose bolts). Stripping threads also tends to be a catastropic failure mode
because they usually "strip one at a time" in cascading manner that quickly reduces the joint load capacity. These observations
help to justify the general practice, which is to "error on the tight side", so long as the engaged thread length is adequate. A final
note on joint shear loads is needed. Bolts are intended to be tension members, so large shear loads can be very troublesome.
The only resistance for shear loads is friction between the joint halves, which suggests a large number of bolts and high clamping
forces. The designer should consider the common practice of "cross bolting".
A related area of great interest is designing for fatigue loading. Since the fatigue strength is so much lower that the yield strength,
the designer is often tempted to consider low bolt preloads, for fear of fatigue failures in the bolts. However by clever joint design
(low C) the alternating loads in the bolt can be significantly reduced. The joint alternating loads remain high, but it is in compression,
where fatigue is rarely a concern. So with a large number of bolts, and a large preload the ratio of bolt alternating to mean stress
can be reduced to a low ratio where the bolt material failure is governed by yielding, rather than fatigue.
Intro
Page 3
This calculation doesn't provide the number of bolts, but usually, many small bolts are better than a few large bolts.
The follow-up step is to tighten these bolts as much as possible, for fear that they might come loose in service.
While there are a number of more subtle joint design issues, this very basic design approach is surprizingly good !
Most textbooks apply the safety factor to the bolt strength, while most practicioners prefer the safety factor on joint loads.
Simply stated, this is because a safety factor of 1.2 satisfies nobody, while the safety factor of 4 means bolts may come loose.
When a bolt is tightened, its grip is stretched by the bolt preload force (Fi). At the same time, the joint (or members) are
compressed by this same preload force (Fi). When an external load (P) is later applied to the joint, the bolt stretches more,
the second Figure. As the applied load is increased, the joint clamping force will approach zero, where upon the joint halves
will separate or unseat. Beyond the unseating load, the bolt tension (Fb) is equal to the joint load (P) ...as if the joint were
joint in compression) is the basic method used to evaluate bolted joints. The first two Figures are combined in the third,
to provide a simple graphical basis for understanding. From this graph, it should be apparent that the designer would like
to choose the bolt preload that roughly matches the bolt strength to joint unseating load. This is the justification for the
opening statement, ...that the needed bolt section area (At) is roughly the joint load (P) divided by the proof stress (Sp).
The somewhat curious note is that bolts are often preloaded to 60-90% of proof strength, and then a similar load can be
as the force divided by resulting deflection. The bolt is a cylinder that experiences uniform stretch, which means the spring
constant (Kb) is simply the elastic modulus (Eb) times the tensile stress area (At) divided by the grip length (L). The
distribution of stresss and strains in the joint is both very non-uniform, and a subject for lengthy analysis. The common
practice is to define an '"equivalent spring region" around each bolt. as illustrated by the cones in the second Figure. The
small ends are meant to represent the head and nut areas, while the conical shapes reflect the spreading of stresses in
the middle of the joint. A simple approximation for the spring constant of this volume is provided on the right. To avoid
very lengthy analysis, this should be considered a reasonable approximation that is neither precise, or highly repeatible.
equal (assuming the joint doesn't unseat). This means that the ratio of spring force changes is the same as the ratio of
) by the bolt proof stress (Sp)
And, of course, a design safety factor must also be included !
* When tightening the bolt, the force (Fb) stretching the bolt must be equal to the force compressing the joint (Fm).
) must be equal. Also, the
) compression, illustrated by
parallel spring model (bolt in tension, and
(C) is obtained from the parallel spring model. A spring constant (K) is defined
(C) is obtained from the parallel spring model. The joint and member spring deflections must be
Intro
Page 4
So, for example, if the bolts are loose, the allowable joint loads would be limited by premature joint unseating
At first glance, it would appear that the desired preload is the value that would maximize the allowed joint load is the case
that would produce simultaneous failures by all four modes above. However, this approach tends to be modified when the
consequences of each of the failure modes are considered. The first two modes tend to be somewhat "forgiving", while the
last two tend to be more serious concerns. With ductile materials, a small amount of yielding will stretch the bolt or crush the
joint, which often has the net effect of relaxing the preload (Fi) to the value that should have been selected. However this also
reduces the service safety factors. If these chosen safety factors were generous, the results may still be acceptable.
Joint unseating tends to be more catistrophic because even small side loads will cause abrasive wear of the joint asperities
which very quickly reduces the bolt preload to zero (loose bolts). Stripping threads also tends to be a catastropic failure mode
because they usually "strip one at a time" in cascading manner that quickly reduces the joint load capacity. These observations
help to justify the general practice, which is to "error on the tight side", so long as the engaged thread length is adequate. A final
note on joint shear loads is needed. Bolts are intended to be tension members, so large shear loads can be very troublesome.
The only resistance for shear loads is friction between the joint halves, which suggests a large number of bolts and high clamping
A related area of great interest is designing for fatigue loading. Since the fatigue strength is so much lower that the yield strength,
the designer is often tempted to consider low bolt preloads, for fear of fatigue failures in the bolts. However by clever joint design
(low C) the alternating loads in the bolt can be significantly reduced. The joint alternating loads remain high, but it is in compression,
where fatigue is rarely a concern. So with a large number of bolts, and a large preload the ratio of bolt alternating to mean stress
Math
Page 5
Background Discussion & Comments Using these .xls worksheets
BOLT INSTALLATION * The intent was to automate the joint analysis details,
* bolt torque to Initial Bolt Tension relation (approx) so the user can "what if" pick the % of yield for the bolt and thread
… bolt tension = joint compression * The tab labels indicate: bolt mat'l, grip mat'l, and thread mat'l
note: the running torque of locking features should be added to this desired preload * The left block provides the bolt installation torque
* Bolt tension to nominal stress (approx) relation * This torque is the lower of bolt strength or thread shear limits
* The 2nd left block provides the joint preload (or clamping force)
* The remaining blocks list the max JOINT force for each failure mode
SUBSEQUENT JOINT LOADING IN SERVICE * The joint will either unseat first, or bolt will yield first ...use lower value
* bolt tension increases & joint compression decreases * For other cases, copy to a new sheet and edit the materials table
* To alter the (L/D) ratios, try changing columns C & I, or H & D
...bolt force
...member or joint force
COMPRESSIVE GRIP YIELDING UNDER THE HEAD
* Head bearing stresses (or face compression)
TAPPED THREAD FAILURE IN SHEAR
* local stresses include shear, bending, & contact loads
G (inlb) ~ 0.2 d Fi
Sb = Fb / At ...At = Tensile stress area (from tables)
* bolt tension (Fb) to Applied Joint Load (Pmax) relation
Fb = Fi + C Pmax
Fm = Fi + (C-1) Pmax
where: C = Kb / (Kb + Km ) ...the joint stiffness fraction
bolt stiffness: Kb = Eb (pd²/4) / L
joint stiffness: Km ~ Em (5p/16) (d+L/4) ²
* Bolt Yielding: Fb -> SyAt
* Joint Unseating: Fm -> 0
Fb = Shd (p/4) (D²hd -OD²)
* theoretical shear: ~ Ssy exp(-kz/L) …which is changed by local plasticity
* we might estimate shear profile as a trapeziod: ~ Ssy (1-k'z/L)
however, this is usually simplified to a triangle: Fthd ~ Ssy p OD (L/2)
* handbooks list tensile yield, so Ssy ~ 0.58 Sy (von Mises)
* In pullout test of ductile threads, we use: Ssut = f(Z/L) ...constant Ssut
but std thread form has p/8 flats, so : Fthd ~ Ssut p OD (7 Lthd /8)
Math
Page 6
* The intent was to automate the joint analysis details,
so the user can "what if" pick the % of yield for the bolt and thread
* The tab labels indicate: bolt mat'l, grip mat'l, and thread mat'l
* The left block provides the bolt installation torque
* This torque is the lower of bolt strength or thread shear limits
* The 2nd left block provides the joint preload (or clamping force)
* The remaining blocks list the max JOINT force for each failure mode
* The joint will either unseat first, or bolt will yield first ...use lower value
* For other cases, copy to a new sheet and edit the materials table
* To alter the (L/D) ratios, try changing columns C & I, or H & D
A286-Al
Page 7
pick PRELOADS: 73% of BOLT YIELD Strength for JOINT SHEAR:
73% of Tapped Thread SHEAR YIELD Strength
APPLIED DESIGN (joint) LOADS
..Unseat JOINT ..YIELD BOLT ..SHEAR thread
1.5 2.0 1.5 2.0
BOLT 1.5 2.0 BOLT 1.5 2.0 [smaller value ..unseat or yield first?] 1.5
ANSI size (in lb) (in lb) (in lb) (lb) (lb) (lb) (lb) (lb) (lb) (lb) (lb)