Tensa Fab. A short summary of this paper. 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 E3 To account for it the section modulus is taken as 1. The connection has to transfer a factored shear of kN. Use bolts of diameter 20 mm and grade 4. E5 1 The recommended gauge distance for column flange is mm. Therefore required angle back mark is 50 mm. E5 with vertical pitch of 75 mm 4 Check bolt force Similar to the previous case, the shear transfer between the beam web and the angle cleats can be assumed to take place on the face of the beam web.
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. The plate would have a similar failure line but it is thicker than the web the material is the same , and hence it is useless to also check the plate. It must be noted that DIN rules do not provide guidance to calculate block shear, so we choose to follow the EC method.
For our case, where we perform only manual checks, some engineering judgment is suggested to narrow down the possibilities. If the maximum eccentricity is at the bolt group, usually the center of the bolt group is considered; however, taking the far bolt vertical row is more conservative probably too much.
Here, as in SCS, only a resistance check is performed; otherwise the discussion would extend to the entire structural analysis, not only the connections. Thus it is left to the engi- neer to evaluate for a possible interaction luckily rare with global instability issues in the beam lateral and torsional buckling.
The notch in the section involves a reduction of the beam bending elastic mod- ulus from to cm3. Taking as maximum eccentricity for the notched beam the distance between the connection axis and the edge of the notch we prudently Figure 4. The DIN rules allow amplifying the elastic resistance of a factor that is the min- imum between 1. The net section is a T in our case and the ratio is over 1.
Also, a throat of 6 or 7 mm could be appropriate. The value equiva- lent to 0. As mentioned, the erection looks easy because the length of the secondary member is less than the available clearance between the primary members. If the connection axis is, as it usually is, in the primary-member axis, the bolted group at the secondary is the more eccentric and, therefore, the more stressed.
This translates into normally having the same or a bigger number of bolt columns than the group at the primary. Usually, the two bolt groups have the same bolt size, pitch, and gauge. The solution shown in Figure 4. The beam material is S For the plates we will try to use S, with class 8.
Designing three rows of M20 as in Figure 4. Since the axis is on the main member, the external bolt group here called group 1 will be more stressed than the one next to the primary group 2 , which is the reason for the initial choice of trying two columns of bolts in group 1.
Now we check the plate welded to the main beam. Leaving 35 mm on the other side edge of the two plates , we cannot design a larger value because otherwise we would have a clash with the weld.
The block shear coming from tension tearing out the web as in Figure 3. Also the plates are adequate see SCS. If the tension is uni- form, the strong-axis bending moment varies depending on the connection axis location. The most stressed sections might be, generally speaking, the external, but the load is transferred by bolts, and therefore we consider the section at the bolt group center.
This bending moment is then the same as the one evaluated as 32 kN mm. This weld is minimally stressed being near the axis of IPE , the eccentricity is practically zero , and therefore the check can be omitted. If the connection as in Figure 4. If the pin connection is considered at the main beam, the plates and bolts especially will be loaded by an eccentricity moment that the designer must take into account.
Notches are possible, obviously, in the secondary beam, on both the top and bottom. The shear end plate, generally speaking, might be applied in several situations e. This joint would not allow any clearance for erection in the secondary-beam axis direction and hence the secondary is normally shortened by 1 mm or so on each side to allow its insertion on-site and to account for some possible additional overthickness given by, say, galvanization.
Bolts in shear, possibly also in tension; 2. Bearing for the plate and its counterpart on the main beam; 3. Block shear for the plate and its counterpart on the main beam; 4.
Resistance of the plate and its counterpart on the main beam, in particular, shear and bending moment for the plate possibly also axial forces and shear for the main beam possibly also tension and bending moment ; 5. Shear local resistance of the secondary near the header plate, possibly also resistance to tension; 6.
Weld failure. Similarly, the bending moment generated by an axial load can be evaluated see example in Section 4. In order to satisfy structural integrity requirements [13] proposes for at least one side of the connection i. Note that this criterion is also a measure of the ductility and rota- tion capacity of the joint. Since this check translates into keeping some additional capacity for opposing tension forces, Ref.
The recent [17] proposes also some formulas see Example 5. The plate chosen is 8 mm thick, similar to the beam and column webs and not too thick in order to help rotation if possible. Again, though, a rigid approach would mean also checking the connection rigidity.
The tension request is negligible — from SCS, choosing a very simple method like the neutral axis, not through the center of gravity see Section 4.
Let us then notice that the eccentricity is also next to zero if we take the column axis as the connection axis, the eccentricity is half the web thickness, i. As we saw in Section 4. It can be used in beam-to-beam connections as well as in column-to-beam joints see Figure 4. In order to help the rotation, it is also recommended that the distances between bolts not be short.
It is therefore sometimes convenient to add some seated connections as temporary support for erection operations. Generally speaking, though, the welded variant is not very popular. Another infrequent alternative is to make the connection with only one angle, which is clearly less resistant bolts work in only one shear plane and causes more design issues the bolt group on the primary member is also stressed by an eccentric moment in the bolt group plane but there are evident advantages for erection.
To eliminate the latter problem, T-shaped sections might be used instead of L-shaped sections. The connection with the primary member shares many elements with the shear end plate see Section 4. Compared to shear end plates, if the connection axis is taken at the bolt group in the secondary not recommended but possible , the bolts also have an out-of-plane eccentricity see Section 4.
This assumption also brings a bending moment to the angles and the primary member torsion, if it is a beam and so does not appear to be the easiest way to check the joint. Generally speaking, double-angle joints have good ductil- ity and can assure valid structural integrity due to the good capacity in horizontal deformation the angles will stretch if overstressed , thereby allowing force redis- tribution.
Since there are no welds, the only relevant fragile limit state to take care of is bolt shear. Our scope is to check that the proprietary tables used by the fabricator to dimension double-angle connections are also acceptable for the mentioned project. The tabulated values for the resistance of angles and bolts the values already include resistance factors are, prudentially considering A as the bolt class, Hence, 6 mm is chosen to guarantee good deformation capacity and ductility.
It is also noted that summing the thickness of the two angles the total is 12 mm will go well over the web thickness of the IPE The values in the table have a vertical pitch of about 75 mm 3 in. It is decided to adopt 70 mm as pitch which slightly decreases the bolt group lever arm and thus its resistant capacity but the check margin is so ample that there is no concern and 35 mm as the distance from the top edge for the angles more than 32 mm and, there- fore, safer.
Again from the AISC table, the bolt vertical axis is considered as 57 mm from the angle corner and we round this value to 60 mm: This worsens the eccentricity a little but it is feasible considering the ample margins a mm choice would be acceptable and more adherent to the table. In the beam, the distance becomes 50 mm, higher than the 45 mm previously considered.
Clearances seem good enough to guarantee the necessary access during erection the bolts on the primary-beam web must not clash with the bolts on the secondary beam web.
The AISC tables also give capacity values for the main beam. It is, however, necessary to make a few additional considerations related mainly to the connections involving angles, a widely used solution. This is the approach suggested also by [3]. Actually, only part of the angle transmits the force shear lag; see Section 3.
When this is needed this is a design con- sideration related to members and, therefore, not in the scope of the book , there are two distinct situations as explained in detail by [3]. Buckling will therefore only happen according to X—X or Y—Y, which can be a substantial design advantage. This applies, for example, to double angles with a b Figure 4.
This is typical in trusses, so this situation applies in most cases. The connection is usually made by using a couple of bolts likely the same size as the bolts in the end connections. The distance between consecutive intermediate connec- tions is calculated so that its ratio with the minimum radius of gyration of the single angle i. In a similar situation, the connections either intermediate or at the ends must take shear forces without allowing movements inside the bolt hole hence friction must resist or hole tol- erances must be very limited.
A comprehensive treatment of the forces to be considered in this kind of connection is given in [3] while not much exists in international standards. AISC [1] only provides some formulas of the equivalent slenderness depending on friction or not as well as tables with bearing capacity as a function of the intermediate links. Practically, also for this case, connectors at 50 times the minimum radius of gyration and bolts as discussed, similar to end-connection details, are normally seen. Again, the reader is referred to [3] for detailed calculation instructions.
For the equivalent slenderness, recent instructions of [20] say, for example, that if the distance is less than 15! Relying on the direct support to transfer gravity forces and having bolts to resist other horizontal forces and possible bending moments provide an impression of simplicity and strength that draws interest. Even the erection, counting on the support, is facilitated.
Horizontal forces applied to the beam by secondary members or by plane braces might generate torsion. Generally speaking, we can then say that this kind of joint is not recommended for relatively important projects but it can be found in small jobs like mezzanines, agricultural structures, and small canopies.
The most classic use is Figure 4. The two forces, unless there is some additional axial action in the beam, are equal and opposite. The reader is referred to the discussion in Section 4. In this case, the shear is the sum in absolute value of the shears obtained on each side. Taking a cue from the interesting discussion in [10], we show in Figure 4.
It has to be noted that an alternative used in the United States for the supple- mentary web plates called web doubler plates in the United States is to weld a couple of plates at some distance from the web as in Figure 4. This can help to avoid problems with galvanization see discussion in Chapter 6 when this treatment is expected. If necessary, the continuity plates i. For the welding detail, check Figure 4. The design practice does not apply the shear to the bolts working in tension, especially those in the external areas of the con- nection, because they are supposed to work at their maximum tension capacity.
It is therefore conve- nient and easier for design to assign the shear to the bolts in the compression zone, which is otherwise lightly loaded. Haunches might also be utilized to enhance the local beam resistance. The force symbols as in Figure 4. The engineer must then focus in designing the end plate, bolts, and welds. In particular, Ref. For the part that is perhaps numerically more delicate in the design of the end plate, that is, the thickness of the plate itself and the size of the bolts, Ref.
Paraphrasing the concept, EC3 provides a precious general method that requires, for the T-stub design, many steps and comparisons with minimum values to apply.
The reader is referred to the sources [21—23] for detailed formulas. Bolt tension 2. End-plate bending 3. Beam web tension 5. Column web tension 6. Beam web to end-plate weld tension 8. Column web panel shear 9. Column web buckling Beam web to end-plate weld shear Bolt shear Bolt bearing.
The designer will possibly have to evaluate additional actions, for example, on the beam weak axis, if they are not negligible. According to [10], it might be convenient to start from the column side considering the two top rows in tension as reacting with the same value as a group in the case of an extended end plate. Finger shims to be inserted during erection can also be contemplated.
The beam has a 5. The weak-axis moment and shear can be considered as negligible. The com- pression is also negligible and we will not take it into account when checking tension limit states but will include it for the compression checks.
An acceptable geometry for the connection and so a good starting point could be the one shown in Figure 4. In this case, we assume that the purlins lean on the beam but not in the zone where the beam connects to the column and the roof panel is above them so the end-plate extension is applicable and is not an obstacle to other construc- tion details.
In other words, the purlins can be positioned right before the column connection or right after, on the other side, as in Figure 7. As per EC instructions, it can be assumed that in a beam-to-column bolted end-plate prying action develops. We begin from the column, checking the tension of the bolts, chosen as M16 it is not a rule but quite often the bolt diameter is larger than the plate thickness. So far, we have not considered if the compression part of the joint can develop the forces necessary to have the above moment, so we will check this now.
From Table 3. Its fabrication being a little more complex, we decide to follow Figure 4. The value we just found is based on an approximate zeq see later in this example for a more precise evaluation.
The same applies to the web weld the reader can check it by SCS. The limit for a pin connection is instead 8. Note that sometimes end plates that can restore the full bending between consecutive sections are called splices. There are several possible variants, some of which are shown in Figure 4. The solution on the bottom of Figure 4. The bending moment capacity of a similar connection is very good for positive bending moments, taken by the lower cover plate, but quite limited for negative moments i.
The splice position of a similar joint must therefore be chosen with care depending on the envelope of the design moments. Other variations might consist of some welded parts, to be realized either in the shop or on-site. For example, some plates as in Figure 4.
Another option when a full-strength connection is requested might consist in using a couple of plates to temporarily preassemble the parts, but then the members are fully welded e.
Some ideas and examples to solve the problem are illustrated in Figure 4. The Steel Construction Institute [10] recommends designing the connection with the bolts in friction at least to service loads in order to avoid rotations due to the bolts slipping inside the holes.
The structure could be part of an industrial or residential project. Even an external safety stair could deal with a problem like this. The column is best interrupted, for erection reasons, about 1—1. A mm inter- nal plate avoids any interference see Table 6. The moment on the external plate will then be half the design weak-axis bending moment plus the bending given by the eccentricity times the weak-axis shear the joint axis is considered at the contact of the column parts.
The addi- tional moment will also stress the bolts. SCS shows that the moment is negligible, adding only a few percentage points of additional stress in both the bolts and plates. Let us then check the tension for the internal plate to which we assign, con- sistently with the resistant sections in the bolt group check, one quarter of the tension force, that is, kN.
We have Section 9. The choice is made to let this key element of a multistory building have an ample safety margin, avoiding solu- tions that might look too thin.
The reference length for instability can be taken as the maximum distance between consecutive rows of bolts the governing situation is usually the distance between the bolt rows across the joint axis, that is, the end surfaces. The reader is referred to the considerations in Section 4. To give more ample tolerances during erection, fabricators sometimes ask the engineer to put double-bolted plates see Section 4. If the braces also work in compression and are made of double angles or chan- nels, see the considerations in Section 4.
As mentioned in Section 2. The scope is to determine a set of balanced actions for the vertical connection which includes gusset-to-column and beam-to-column joints and the horizontal connection gusset-to-beam. The equilibrium of the forces must be granted in order to assign any bending moments to one or more of the connections in the system.
For congruence, the vertical connection bolted as shown in Figure 4. The same consideration is valid for the UFM. In those applications there is a moment to be applied somewhere in the joint. In the frequent case of a joint welded to the beam and bolted to the column, the moment is assigned to the gusset-to-beam connection. In this regard, the engineer may specify to use suitably sized turnbuck- les normally commercially available or the like.
The request by the fabricator and erector is to have oversized holes for bolts to ease the erection. The connection will then be designed as slip resistant at serviceability adequate for this structure. Hence, six bolts are necessary and they resist about kN. Considering an edge distance that is twice the bolt diameter suggested minimum by the author for braces , the bear- ing check becomes 0. The tension resistance is then 0.
The tension resistance for the net area governing is then 0.
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