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Need an account? Click here to sign up. Download Free PDF. Tensa Fab. A short summary of this paper. Download Download PDF.

Translate PDF. E1 Try the arrangement shown in Fig. Assume that the flange splices carry all of the moment and that the web splice carries only the shear. The splice is near a point of lateral restraint.

The ends are not prepared for full contact in bearing. ISHB This is conservative and helps the project budget. If an engineer who is not familiar with structural steel develops a model with- out careful consideration of the lateral load resisting system and the connections among members, it could severely impact the project. If the entire model has rigid connections, the structure could be underdesigned and unstable if the joints are not correctly dimensioned and realized as fully restrained.

Also, in the event that the joints are correctly fabricated as rigid, the competitive price of a similar fully restrained system with complex and labor-intensive connections is suspicious. According to the classical elastic method, it is not required to check connection rigidity because the experience of the engineer is enough to assess this. However, some standards EC primarily have started to ask for an analytical check of this component. They are ini- tially able to resist bending moments, more or less relevant in absolute value.

The engineer must indeed learn that the experience in the sense of the history of structural engineering and the ductility of the material makes this kind of con- nection representable as a pin, and years of structural steel buildings have shown that this approach is both sound and reliable.

This also means that it is not con- servative to assign calculation moments to these kinds of connections, especially if those bending moments are essential to the overall stability of the structure. In fact, the steel is ductile and the material will become plastic when the yield limit is reached and there are no brittle or buckling behaviors. This means that the connection will develop into a hinge, thus redistributing forces.

This explains why some joints that do not look like pin connections are represented as such in the design practice. As mentioned in the previous section, intermediate behavior semirigid is dis- cussed, for example in EC and AISC partially restrained PR joints , but it is crucial that the designer comprehends the plastic hinge concept that has been used for many years in steel construction.

With this in mind, we take a closer look at two typical examples of welded connections in trusses and base plates. This method was used several years ago, as seen in the example of the Milan railway station in Figure 1. Many books, including [2], agree on this concept, explicitly articulating on the subject.

Source: Picture courtesy of Massimiliano Manzini. Source: Taken from [2]. The reason is that a plastic hinge will form: Even if the connection is initially rigid and able to resist non-negligible moments, it becomes a hinge after the material yields. Theory and Design of Steel Structures. Therefore, this chapter will not present formulas; rather the formulas will be provided in Chapter 3 and, to a lesser extent, in Chapter 4.

Here, we will discuss ideas and concepts, some of which are not always clear and intuitive to a designer not very experienced with steel. Under this connotation, joints can be hinges pins , rigid fully restrained connections, and semirigid joints intermediate behavior , as illustrated in Figure 2. Another possible distinction from a seismic point of view and even, gener- ally speaking, to reach a good performance design is with regard to ductility. This assessment is done by checking all the limit states to see if the governing limit state is ductile or nonductile.

From an experimental point of view, ductility is measured by the deformation usually rotation capacity of a joint before its collapse. Many other ways of sorting joints are possible, such as welding or bolting, or depending on the kind of connected members e. See Table 2. Table 2. Actually some important considerations should be made because, according to the scheme assumed in connection design, forces can change.

Let us consider the possibility that the FEM model will connect joints by default along their axes. Although commercial software is available, which allows the connection location to be changed, since this process can be time-consuming, it is not done in many situations. The exact pin location can be taken at any of the following positions Figure 2.

On the column axis 2. Let us also notice that the two cases mentioned above are the ones usually referred to because one minimizes the eccentricity on the column making it zero and the other minimizes the actions on the bolt. Here there are three possible basic schemes Figure 2. Another example is a brace connection to a column and beam see Section 4.

At this point it is important to stress that any situation can be chosen if the balance of forces is correctly imposed. As discussed, the actions on the connection elements can be reduced to the expenses of actions on the column, or the opposite can be done according to preferences. At this point, if possible, the engineer could try to move the axis of the connection to reduce the forces on the bolts due to eccen- tricity.

If there is no particular element design to be minimized, the engineer will likely choose the location of the hinge as suggested by his or her common sense. Again, though, this is not the only way; it is just one of the possibilities. The real distribution of forces is the one that will maximize the load, in other words the one that can withstand the maximum actions. An example given in [2] will help in understanding this idea: if some weight is supported by three steel bars, intuition says that the load will be uniformly divided.

However, if the central bar bears no load, a possible solution for this design problem is to divide the load between the two external bars, which bal- ances the distribution of weight and, therefore, can be deemed as acceptable. Assigning some percentage of the resisted load to the central bar, we can also obtain an acceptable design, due to steel ductility. However, it is true that the solution that will maximize the allowable load is the one where all bars take the same part of the load, and in fact this is the closest to the real solution and yet, once again, it is not the only one available.

This is true globally not only for the structural system but also locally for the connections. This concept will help solve problems in nonordinary connections and will also help in understanding the response of complex systems. A possible example is a connection between plates that is realized with both bolts and welds Figure 2. If the weld breaks nonductile , the bolts will support the load but, also in this case, the whole action must be resisted.

The result is that a design that divides the forces might not work and could eventually have serious consequences e. Ductility allows for better use of steel resources, exploiting the plastic behav- ior recall the example of the three bars in Section 2.

However, even a nonductile design, if correctly sized, is acceptable. Generally, it is well known that it is good if a ductile limit state governs the design so that a redistribution of forces is possible if the foreseen values are exceeded. The latter has a collapsing mechanism that interrupts the transfer of loads, ending in collapse. Additional comments about these as well as other limit states are given in Chapters 3 and 4. In other words, what is the path of the load when transferring from a secondary member to a primary member?

It is important to consider this because it can uncover the possible problems a joint can experience. Consideration of the load path is fundamental in the design of connections and to understand the behavior of the joint, so as to avoid forgetting some local checks and thus prevent dangerous blunders. The example in Figure 2.

Following the load path can avoid serious design errors, as in Figure 2. Let us also remember that the forces we use in our FEMs are based on mere guesses. Especially for steel structures it is well known that commonly used elastic theories would be wrong without consideration of plasticity see Ref.

It is appropriate to reiterate that the assumed load path is just one of the options within the many possibilities available; each is acceptable if equilibrium and con- gruity are maintained. In short, only after thorough testing can the formulas discussed in this chapter e.

A bolt is hence commonly designed considering only shear, taking as a limit a value proportional to the ultimate resistance as determined by tests. This value is approximately 0. In the second case, the eccentricity and its moment can occur unexpectedly because of poor design. Those bending moments are parasitical and come out of inattentive design or detailing, for example, in trusses or brac- ings where the detailer or the fabricator has not been correctly briefed about the possible problem.

If the design sketches represent the neutral axis and the detailers are correctly instructed, this category of parasitic eccentricities can be avoided.

If the eccentricity is unavoidable due to fabrication, erection, or other reasons , it is important that the detailer informs the engineer of all eccentricities present in order to make the necessary recalculations. The advice is consequently to discuss the matter with the fabricator and choose accordingly. See Ref. Figure 2.

This is documented for example in [11]. Pretensioning comes at a cost because one method must be applied see Section 6. For all these reasons, it should be prescribed only when necessary.

There are US guidelines Ref. Eurocode requires pretensioning for categories B, C shear with fric- tion resistance respectively for serviceability and ultimate limit states , and E pretensioned joints working in tension.

If pretensioning is not considered in design checks it can occur if there are friction-resistant connections , it becomes a personal decision whether to prescribe it or not. Thus, even though there might be some performance improvements at a cost , pretensioning is not strictly necessary. Section 6. For example, if a beam frames into a column but there are also other beams or braces on the other side of the column, it is not clear how forces divide and, for example, what is the shear taken by the col- umn.

This means the engineer should check how forces from the calculation model should be vector summed. The problem is that, sometimes, depending on the local bidding regulations, the model is not available because the connection designer is not the designer of the structure.

The construction design drawings issued to fabricators that design connections should provide the forces case by case rather than as it occurs frequently simply giving the maximum and min- imum absolute values or it could result in incorrect transfer forces see some interesting examples in Appendix D of [12] in addition to making the design too conservative and uneconomic.

Analogous sit- uations can occur in alternate cases too, especially if bracings are involved see Section 4. One advantage is that pretensioning makes sure there is no separation unless loads go well beyond service loads. As sketched in Figure 2. The force P Figure 2. The exact value when parts separate depends on the prying action that, as we will see in Chapter 3, is based mainly on the connecting plate thickness.

The two cases in Figure 2. Empirically, when there is a separation of connected parts as illustrated in case Figure 2. For a more detailed discussion of this the reader is referred to [13]. Notice that even in the prying action case illustrated in Figure 2. Brussels: CEN. Joints in Steel Construction: Moment Connections. Structural Analysis, vol. New York: Wiley. Calcolo plastico a rottura nelle costruzioni. Practical Yield Line Design. Joints in Steel Construction: Simple Connections. Steel Construction Manual, 14e.

The connections are indeed made by components and each of them needs to be proven for strength, stability, deformation, and anything else that gives satis- factory performance and safety to the structural system.

This does not negate the need for engineers to subsequently make sure that the connection deformation capacity is consistent with the design assumptions. For the typical joints described in this book, the instructions here given, joint by joint, coupled with member displacements in other words, joint rotation in the standard limits which should be by rule supposedly guarantee that the defor- mation capacity is acceptable.

For the entry of Sj in the global analysis model, refer to the indications in [1]. For an in-depth analysis of the matter, the reader is referred to various texts e. A typical example is a fully bolted truss i.

Even if special care is dedicated to tightening the bolt under its own weight e. One possible applicable solution to prevent this is by prescribing the necessary precamber in the shop drawings. Another possibility as already mentioned is to pre-erect some parts on the ground where there is no gravity force deforming the structure.

It is necessary to highlight that the shear failure of the bolt is a brittle limit state, and therefore it is not desirable that it control the design i.

The discussion in Section 2. If the threaded portion is in the shear plane type N bolts in the United States, where N stands for iNcluded , the value has to be divided by 1.

See Table 3. The concept of bolt shear failure is clear and intuitive while two concepts just mentioned are less intuitive and need to be discussed: failure also depends on the number of resistant sections and the presence of the bolt thread inside the shear plane. More detail of those concepts will be provided in the following sections. However, the usage of bolts with the right thread length matched with the competence to give to erectors, who have to be mindful of this important detail can lead to savings, especially in Table 3.

Table 3. Imperial bolt in. As for the previous point threads included or excluded , this notion can be used to contain the shear stress of bolts. German DIN now superseded but here referenced because it is still used and it sometimes provides interesting advice supplies an interesting indication regard- ing the potential problem for a bolt in double shear but with only one shear plane crossing the thread.

DIN recommends evaluating the two resistances sepa- rately, then summing them and comparing the result with the applied load. For double-shear connections with packings on both sides of the splice, t p should be taken as the thickness of the thicker plate.

According to [8], packing plates should not exceed a quantity of 3 and should not have a thickness less than 2 mm. Bolt: Class 8. Not recommended for structural applications. AISC, as previously mentioned see Table 3. The check of the resistant net area of the bolt independent of the presence of a partially threaded shank takes place in relation to simple tension as well as to ten- sion due to moments, both possibly increased by prying action see Section 3.

Additional safety factors are provided for this limit state with regard to the pos- sible local parasitic bending moments usually accompanying the tension loading of fasteners, which explains why the actual resistance is considerably less than the material resistance. The tension failure of the bolt is not as brittle as the shear failure since there is elongation of the bolt prior to the failure.

DIN recommends the lesser of the two values given by ASch fy,b,k 1. Consider that M10 should not be used for structural design and that currently the recommended types for minor size are M12, M16, M20, and M The second term Ab F nt shows that the resistance cannot be greater than the case where only tension is included.

It is necessary to report that, in order to verify combined tension and shear, Ref. For combined actions in which the shear force is resisted by friction, see the next section.

The design of a slip-resistant connection can be realized at the serviceability limit state category B in [1] or at the ultimate limit state category C according to EC. In either category B or C, bolts have to belong to classes 8. For bolts conforming to these standards, the preloading force used in the previous equation is taken as all symbols familiar 0.

Case ks Holes with standard nominal clearance 1 Oversize holes 0. Both bolt bearing and bolt tearing depend on the material, bolt diameter, plate thickness, and hole edge distance.

The last two variables are certainly the most easily adjustable and in particular the increase in distance between the hole and the edge of the plate is the easiest and cheapest to change.

The distance between the axis of the hole and the plate edge is usually designed as 1. If there is more than one bolt in the direction of the load transfer, then it is necessary to evaluate the failure also with regard to the spacing of the bolts, since bearing can occur for inner bolts too and it directly depends on the spacing of the bolts. Bolt tearing Figure 3. Figure 3. The bearing resistance of every single bolt should be compared with the limit value. Refer to Figure 3. When using the equations above, the EC approach implicitly includes a check of the cross-section and application of these expressions also in compression controls this tear-out would occur only in tension conditions and bearing too is usually critical in tension because in compression the edge distance is not a factor.

The material collapses according to the angle shown in Figure 3. AISC also insists on checking the resistance against the bearing strength, which is equal to 2. F F Figure 3. In addition, if there are two resisting sections, the dou- ble element will have the total double thickness in calculating the resistance or half the force if this is checked against only one plate.

For a comprehensive calculation, the check must be executed in both perpen- dicular directions i. Eurocode recommends reducing the reference thickness to a value equal to half the countersink depth. Source: Photo courtesy of J. Swanson and R. Leon, Georgia Tech. Operationally, it would be necessary to check the block shear in both direc- tions unless there is either only a simple axial force or shear with no eccentricity.

This is currently poorly addressed in provisions that do not provide any special instructions on how to perform the check in those cases.

Reference [13] also adds some interesting formulas to check shear and bending interaction of the beam web. First of all, it must be kept in mind that welds have an extremely limited capacity of deformation, so overcoming the resistance of a weld usually activates a mech- anism of brittle type, in particular if the weld is stressed transversely in spite of the increased load that it can bear.

See Figure 3. This kind of design full strength also means that the checks are omitted in the calculation reports. However, it is desirable that the welding failure is not the limit state that governs the design since it does not allow the redistribution of loads.

If weld failure governs, the design structure would be considered fragile. Source: Taken from Ref. It is however interesting to note that the latest AISC indications will reduce this request by comparing the yield strength of the plate with the rupture of the weld, whereby the ductility is reached with a leg not throat! As Figure 3. Beyond this limit it is convenient to use a double-V or K weld see Figure 3. A partial-penetration weld compare Figure 3.

About welding positions see Figure 3. Some of the most frequently used symbols are given in Figure 3. As mentioned, the design checks for welds are various and will not be discussed in detail here, but some general guidelines are given below. The individual components are calculated by dividing the forces that act upon the weld. For commonly used materials, the value is 0. Since 0. In addition, according to the AISC, the strength of the weld can be increased according to the loading angle.

As mentioned earlier, transverse actions lead to a bigger strength at the expense of ductility. A less conservative and more accurate alternative is to calcu- late the plastic or elastic module of the weld, using it to get stresses.

Chapter 4 will present some numerical examples. As for eccentric bolted joints, the AISC manual introduces an elastic method and an instantaneous center-of-rotation method to evaluate welds with eccentric loads. Source: Adapted from EC 3. For a comprehensive theoretical approach please refer to [17], which also deals with situations of torsion or complex stress, and see Chapter 4 for some practical examples.

For information on preparations and beveling of welds, see Ref. It would be desirable to also inspect the bevels before welding. Then the excess red liquid is removed and another contrast or detector liquid is sprayed. This second mixture is usually white so it is clearly visible when the red liquid has penetrated into cracks.

It is only possible to identify the cracks open on the surface. A plate with two bolts working in tension and an additional perpendicular plate is shaped like a T.

There are three possible collapse mechanisms for a T-stub: 1. Only the bolts fail, which means that the prying action is negligible: the bolts share the load and the plate rigid and strong will work in bending as shown in Figure 3. This means that the design of a resisting system can occur in two opposite ways: a Minimizing the action upon bolts at the expense of the plate a thick plate will make the prying action negligible ; this approach corresponds to the collapse mode in Case 3 of Figure 3.

Case mode 2 in Figure 3. See Chapter 6 for some reference values for washers, heads, and nuts in this regard. The last equation tells us that the T-stub resistance is calculated as the sum of the tensile strengths of the bolts. This will be seen for each case in the following sections. Note the presence of f u instead of the yield strength, although it is indeed a limit state corresponding to yield and not to failure: the reason is a better consistency found with laboratory tests because there is con- siderable hardening.

If the elongation of the bolt or the anchor bolt is greater than the length limit, we can consider that there are no prying forces, whereas if it is below the length limit, the prying forces must be taken into consideration. Also note the presence of nb correction of the original [1] that was not providing this term , indicating the number of bolt rows assumption of two bolts per row.

For an anchor bolt, the elongation length is equal to eight times the diameter summed with the base plate thickness, the mortar thickness, the washer, and half the height of the nut. Checking the length is not usually necessary in beam—column joints since [1] says, in a note relating to Table 6.

For the length limit in other cases e. However, for base plates, the latest EC instructions errata of [1] recommend considering the prying action for the check of the anchor bolts but not when verifying the base plate thickness.

In [18] the value 4. Source: From Ref. For emin refer to Figure 3. For other parameters, refer to Figure 3. Source: From EC If the engineer desires to perform a calculation without imple- menting this hypothesis, that is, with the bolts in the corner which is common to base plates , he or she may refer to the examples in [20], also well represented in [21].

For an end plate in the same situation, the equation becomes 0. Also, F TOT must be lower than the force transmittable by the bolt. The method evaluates the thickness in the elastic range and implies a behavior without prying but it is considered conservative. This detail is also called web panel and is seismically critical when it is part of the lateral load resisting system since it is heavily stressed likely inelastically during earthquakes.

The EC formula for calculating the plastic resistance is 0. With reinforcement plates welded to the web also called supplementary web plates in the United Kingdom or doublers in the United States.

In the second case, the plate welded to the web can create problems if the column is galvanized read the discussion in Section 6. The resistance in compression and tension see Section 3. In this second case, [1] allows to consider 1. The following equations are provided in [1] for calculating the exact value the symbols are given in Table 3.

For example, what is called sidesway in AISC is called column sway in EC, but EC does not provide quantitative formulas but only some general advice to prevent it by constructional restraints. See Section 4. Calculating the resistance can have as a reference the yielding or the ultimate resistance of the material, depending on the limit state and, partially, on the ref- erence standard.

As already indicated elsewhere in this book, it is actually preferable, if design forces are exceeded, the plate yields instead of other fragile limit states happen- ing, since yielding allows a redistribution of forces. This means that, on the one hand, it is necessary to check that the limit state is not overtaken and, on the other, that the yielding governs the design: if a ductile limit state steps in before other fragile limit states, it can avoid, for unexpected large forces such as seismic actions, nonductile collapses such as weld failure especially if transversely loaded , shear rupture of bolts, or even the collapse by tension of the net area.

It might be a good optimization, respecting the minimum distances if possible, to make the two areas equal. When performing the check, the designer has to choose between using the elastic or plastic modulus. The choice can be according to the slenderness class even if the elastic is more conservative once any local buckling issue is avoided. The formulas to use vary depending on the standards used, and the engineer is invited to refer directly to the design norm.

Whitmore was an American researcher who, in the s, studied the problem. As in Figure 3. It must be noted that there have been proposals Ref. The Whitmore section must therefore be large enough to take the load. For a full-strength design, the Whitmore section should be bigger than the connected element.

Design equations for the tension resistance of an angle connected as in Figure 3. The formulas are, once again, for angles connected on only one leg and must also be applied for large angles with two or more rows of bolts when they are only on one leg. The AISC provisions have a more general approach for determining the shear lag that is quite interesting because it is largely applicable.

The weld length to connect the plate must not be less than the tube diameter or the width dimension parallel to the inserted plate if the tube is rectangular. Attention must be paid when evaluating the critical area of the tube due to the slot created for inserting the plate: Figure 3.

Eventually, some local reinforcement can be added. If, say, there is a shear tab or any similar situation , it is necessary to verify locally the web of the main member from [13], where Av does not have the factor 2 as multiplier but it is checked against half of the design shear , taking a resistant area equal to see Figure 3. Also, the tie force could be considered as a local capacity check, see Section 3. As a general reference to calculate the unbraced length of a plate, the distance between the CG of the bolt group conservative, otherwise it is more usual to take the near end of the bolted group and the CG of the weld could be taken, depending on the kind of connections, that might have two bolt groups or be fully welded.

A gusset plate for a brace connection is a typical example, with the additional problem that the joint can be in a corner and can have various charac- teristics, as the examples in Figure 3. Several research papers dedicated to gusset plates in compression e. The results are not univocal. Thicker plates classify as compact. Some examples are given in Figure 3. The one in Figure 3.

Using Table 3. The resulting resistance should be greater than the bending moment in the plate more precisely, Refs. Terrorist attacks might indeed generate unexpected load conditions Figure 3. However, the event showed that the structural system was very weak in resisting unexpected loads, quite small in value when compared to the resistance of the building to the gravity loads. In the United States, a special committee is currently studying this kind of problem and the proposal is, for buildings that are tall or in special categories hospitals or sensible targets , to impose some additional requirements that can help guaranteeing a good structural integrity.

Those forces are also known as tying forces. In Chapter 4, suggestions to reach an acceptable structural integrity are given for many kinds of joints.

The reader is referred to Section 2. The lamellar tearing phenomenon can become critical in thick plates that are loaded perpendicular to the lamination plane, for example, with T, corner, and cruciform junctions with relevant welds.

The examples in Figure 3. According to [17], the potential trouble is in fact a design consideration only when the plate is over 40 mm thick, even though some defects have been recorded with thickness around 25—30 mm.

Source: Table from Ref. AISC addresses the problem by reminding about good detailing practices. Since experimental testing is recommended in those cases, it may be best to ask the material supplier for instructions and design tables that indicate where to choose the details of the connections.

References a b Figure 3. Other materials are wood in some roof connections and aluminum. Dealing with the limit states of those materials is not within the scope of the book, but the engineer is encouraged to carefully consider them. References 1 CEN Eurocode 3: design of steel structures — Part 1—8: Design of joints, EN Semi-Rigid Connections in Steel Frames. New York: McGraw-Hill. Oxford: Pergamon. Australian standard — steel struc- tures, AS Sydney: Standards Australia.

General construction in steel — code of practice, 3rd rev. Execution of steel structures and aluminium structures — Part 2: Technical requirements for the execution of steel structures, EN Milan: UNI. Joints in steel construction: simple connections. Structural use of steelwork in building — Part 1: Code of practice for design — rolled and welded sections, BS London: BSI.

Civil Eng. Structural welding code — steel, AWS D1. Design of steel structures, general rules and rules for buildings, EN Recent development in the behavior of cyclically loaded gusset plate connections. References 24 CEN Design of steel structures, plated structural elements, EN AISC 91—, Quarter 2. Bracing connections for heavy constructions. AISC —, Quarter 3. Compressive behav- ior of buckling-restrained brace gusset connections.

Design and behavior of gus- set plate connections. Material toughness and through thickness properties, EN Cold-formed steel, composite structures connections in cold formed steel structures — the testing of connections with mechanical fasteners in steel sheeting and sections, ECCS Guide No. Portugal: ECCS. Eurocode 3: design of steel structures — Part 1—9: Fatigue, EN Engineering judgment will be essential to extend the basic concepts to the most complicated and singular connection types.

The EC codes do not give precise methods to calculate this kind of eccentricity and, therefore, it is convenient to look at AISC methods. Those methods can then be applied to EC design problems. If there is an in-plane eccentricity, the shear will generate a moment in the bolt group. The latter is more accurate but requires an iterative solution that only a dedicated software SCS — Steel Connection Studio can do this or, with some approximation, values in tables see Ref.

Another value that is necessary to apply the equations below is c, that is, the distance, divided in its x and y Cartesian components, of each bolt from the center of the group. The bolt threads are in the shear plane. The bolt group is also loaded by a horizontal kN force as shown in Figure 4. The horizontal force has no eccentricity. In the same way, the forces for bolts 2, 3, 6, and 7 can be calculated but the absolute values will clearly be smaller.

Final results are sketched in Figure 4. Alternatively, in a faster but more conservative way, the contribution of the inner bolts could be ignored and it could be assumed that the design moment is balanced by a pair of couples resisted by the outer bolts, where the lever arm is the diagonal distance between bolts as shown in Figure 4. The forces must therefore be perpendicular to the line drawn between each bolt and the rotation center and the sum of forces and moments must balance the applied shear and the corresponding moment from eccentricity.

To collect further details about the method, which is based on a laboratory load—rotation curve of systems made by bolts and a plate, refer to [2]. Actually, the tables have distances in inches, forcing us to continuously approximate and interpolate the values and, therefore, the pro- cedure is not recommended when using the metric system.

This C value means that an eccentrically loaded group of eight bolts has a global capacity of a group of 4.

The same calculation with SCS brings a resistance value for the bolt group of kN and, therefore, a This method does not require any additional instruction, so we will look at the methods from AISC, which look easier and more immediate than EC. To apply the latter, see Section 4. Figure 4. The lower bolts only share the shear. Combining the tension and shear e.

This makes the equation slightly more conservative than the same equation applied with the bolt net area, since the neutral axis shifts upward with the gross value. The same area will be used in the formulas provided further when evaluating N tension per bolt and Ix. Even with this approach, as in the previous, the bolts will work in shear and tension on the top positive moment assumption and only in shear on the bottom.

Alternatively, a second-degree equation can be written and solved, d being the unknown variable. Another option is using the Microsoft Excel function Goal Seek after writing formulas as a function of d. Since the neutral axis is between the assumed bolt rows, we can proceed otherwise a recalculation with the cor- rect number of bolts in tension would have been necessary. Refer to Section 1. Here, the purpose is to give practical formulas to be used in the design of the elements of the joint.

Before the EC, this was the main method used in Europe too; see, for example the approach in [3]. This behavior assumes that the pressure is uniformly distributed in the plate. To calculate m and n refer to Figures 4. This also means that similar values of m and n optimize the design. It should be noted that if, more conservatively, the elastic modulus is considered instead of the plastic modulus, the 2 under the square root would become a 3.

Let us also point out that the shear on the base plate needs to be checked but it very rarely governs the design so engineers usually neglect this check when computing the necessary thickness t. A large-eccentricity situation brings a separation between the plate and the concrete and, therefore, the intervention of the anchor bolts in tension. In the case of Figure 4.

It will be up to the engineer to evaluate the possible situations and take the most unfavorable with its corresponding y value.

See some possible situations sketched in Figure 4. Axial Load Only If there is only axial compression, the three T-stub regions con- sidered are the ones shown in Figure 4. To get the width of the T-stubs in compression, refer to Section 4.

Axial Load and Bending Moment If there is also some bending moment, EC con- servatively suggests not considering the T-stub below the web. Attention to the direction of the Figure 4. The convention given by EC is to consider the bending moment as positive if clockwise and the axial load positive if in tension therefore it is negative if the load is downward, the opposite of the AISC convention. It has to be noted that [5] calls for the column web tension paragraph related to the web in transverse tension Section 3.

Finally, the formulas in Table 4. Table 4. Please notice that where Mj,Rd is the max- imum result between two terms it is because the moment is negative that the design moment is the least in absolute terms. If columns that are big in size are also heavily loaded, a solution with a double plate as in Figure 4.

A similar double plate has a section modulus that is very high. Eccentricity According to this method, the plate reaction is partial but the pres- sure is uniform. In the previous edition of [4], that is, [8], a triangular distribution of the contact pressure was instead assumed and, though this approach is still possible Appendix B of [4] , it is not recommended because the calculations are a little more complicated the results generally translate into a slightly thicker plate and slightly smaller anchor bolts.

The assumed design hypotheses mean that the pressure has a value f p smaller than f p,max for small eccentricities while f p coincides with f p,max if the eccentricity is large.

If the grout thickness exceeds 50 mm 2 in. Then F Rdu see Ref. Although it may be trivial it is important to remember that anchor bolts are necessary even when the theoretical design load on them is zero because anchors are also fundamental during erection so as to avoid column overturns when positioned during installation. According to US Occupational Safety and Health Administration OSHA regulations for con- struction, a base plate must have at least four anchor bolts and must be able to resist a vertical load of lb kg with a 18 in.

The only columns that do not have to follow this requirement are the ones that weigh less than lbf. The min- imum distance from the foundation edge must instead be more than the larger of 10 cm 4 in. The possible shapes and installation systems to make the anchors capable of resisting uplift inside the concrete are several.

AISC [8] suggests three types, as in Figure 4. Hooked Bar The hooked bar is not recommended unless there is only little uplift or moment because the anchor might fail by straightening and pulling out of con- crete most of all anchors that are smooth since oily substances might be present. Threaded Bar or Bolt with Nut The AISC design guides advise welding or bolting a nut to the anchor in any case some tack welding should follow the bolt tightening to prevent any loosening when the outside bolt is tightened.

Washers in the lower nut are not necessary if following [8] when the anchor material is S or similar. If the resistance of the material is higher, small washers are enough to spread the concrete cone but large washers are not recommended in [8] because they lower the edge distance. The resistant area Apsf is shown in Figure 4. About the design resistance of the steel, similarly to the bolts in tension see Section 3. This is lower than what was considered in the previous edition of the AISC design guide 1 [8], that is, 0.

However, AISC suggests careful assessment of the load combinations and, if necessary, lowering the avail- able load for the friction. In contrast, the EC Ref. However, some standards forbid using the friction when calculating the resistance to seismic shear. Indeed, to make the anchor bolts work in shear some steps must be followed. For example, if the base plate has over- sized holes largely common , the anchor bolt—plate contact for the transmission of forces is not likely to happen simultaneously on all the bolts.

Then, an assump- tion may be to consider only a certain number of anchors to really work e. Alternatively, washers can be welded on-site to the base plate which is sometimes done in large structures but it is not recommended for small and medium jobs because of site welding. If this latter approach is followed, some sources e. There are various approaches to checking the contact pressure: Ref. Instead, [4] says to take either 0. For a solution in accordance with EC the engineer can instead follow the method already seen to calculate the contact pressure transmitted by the base plate see Figure 4.

While the right part of the plate is considered, the k values of the right-hand side will be taken subscript r and similarly in the analysis of the left part subscript l.

When there is more than one row of bolts in tension, the calculation should be performed for each row of bolts. The other limit states forming of a plastic hinge, plate mechanisms, anchor bolt yielding but also excessive contact pressure allow a redistribution of the actions. It is highly advisable to group the bolts and place them with templates Figure 4. If the damage is contained and anchor bolts do not work near the limit, an attempt to straighten them could be done; if the damage is too heavy, one of the above solutions should be applied.

Finally, as discussed in Section 6. For the grout, Ref. If the foundation does not have grout i. It is to be avoided, except in cases of real necessity, to have columns work as cantilevers inverted pendulum on their weak axis.

The lateral resisting systems are portals with rigid bases on one side and braces on the weak side responsible for the remarkable uplift. We consider S as the column material, S for the plates, and class 5. SCS provides a higher value because it also considers the part below the web in the computation conservatively neglected here.

SCS correctly takes the plas- tic resistance and gives us kN. In the tension zone, on the left, the plate must instead be checked for tension bending T-stub, Figure 4. Now, assuming the geometry in Figure 4. Another alternative the method used by SCS would be to make the calculation following the references cited in Section 3.

HEA therefore prying action is possible. In fact, some sources e. However, taking the worst possible situa- tion as per recent instructions see Section 3.

It is underlined that the engineer also has to check not in the scope of this text that the foundation and the soil can resist the design loads.

The T-stub resistance in tension is therefore kN and this is the actual reference value to take since the web column in tension does not govern the design. Let us assume a piece of HEA that is mm long. If we design a pit as in Figure 4. Shear and bending in HEA must also be checked. The governing length is therefore To get a better performance by an AISC-based design, the engineer could shorten the long side of the plate, consequently lowering m and possibly widening the plate to make room for the anchors if geo- metrically necessary.

This has the additional advantage of a much wider tolerance of a precast anchor bolt group because the anchors are installed only at the end, with the steel part already in its position. When connecting to vertical walls, the designer should keep in mind that threaded bars going through the walls can also be utilized. From a design point of view, in addition to the limit states of the steel parts, that is, the anchors themselves and the plate refer to the previous section about base plates , all the checks typical of the concrete must be performed since they are usually the ones governing the design.

In most cases it is advisable to follow the charts provided by anchor produc- ers that sometimes even distribute free software to support the design of their products. The secondary element is a secondary beam if the main member is a primary beam while it is a primary or secondary beam if the main member is a column. This approach seems acceptable. Most of the considerations can be applied later while discussing other connection types without mentioning the options in detail.

It is possible actually the most frequently chosen option to locate the theo- retical pin at the axis of the main member. This scheme minimizes the stress in the column only concentric axial load is transferred or main beam no tor- sion but it creates a moment in the bolt group due to its eccentricity from the connection axis.

It is possible to locate the theoretical pin at the center of gravity of the bolt group. If a beam is the primary member, possibly not balanced on the other side by another sec- ondary, the induced torsion is likely a problem, and hence this choice is not recommended in such cases. It is possible to locate the theoretical pin at any position within the range set by the options above.

Column Beam a Beam Beam b Figure 4. It is possible to weld Figure 4. This might help in inserting the beam during erection Figure 4.

This will allow inserting the beam during erection. False flange Beam Beam Reinforcing plate a b Figure 4. In these instances, a reinforcing plate Figure 4. The geometrical meaning is quite intuitive and consists of avoiding any contact between the parts. The joint rotation capacity Figure 4. If any of these limit states do not govern the design, the joint has good ductility. Instead, Ref. By analogy with the beam material, we choose to take St also for plates. The geometry in Figure 4.

It is considered, to avoid torsion and because this is likely the hypothesis in the calculation model, that the position of the theoretical axis of the connection is the same as the axis of the main beam. With a geometry as in Figure 4.



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