Kane, Thomas. Miller, Duane K. Funderburk, R. Blodgett, Omer W. Leon, Roberto T. Malley, James O. Pugliesi, Raymond S. Williams, David R. Kloiber, Lawrence A. Shaw, Robert E. Heagler, Richard B. Mattingly, John. Azizinamini, Atorod. Shahrooz, Bahram. El-Remaily, Ahmed. Astaneh, Hassan. Following the notation of the Manual. In this case bending in the plate governs.
In addition to the prying check, the end plate should be checked for gross shear, net shear, and block shear. These will not govern in this case. Checks on column web: 1 Web yielding under normal load Hc : 2 Web crippling under normal load Hc : 3 Web shear: The horizontal force, Hc, is transferred to the column by the gusset-to-column connection and back into the beam by the beam-to-column connection.
Gusset-to-beam connection: The loads are kips shear and a kips-in couple. Weld of gusset-to-beam flange: Since The 1. This method does not give an indication of peak and average stresses, but it will be safe to use the ductility factor. The shear is thus This shear is applied to the flange as a transverse load over 15 in of flange.
It does not reach the beam-to-column connection where the beam shear is kips. However, the AISC book on connections AISC, addresses this situation and states that because of frame action distortion , which will always tend to reduce Hc, it is reasonable to use the larger of Hc and A as the axial force. Thus the axial load would be kips in this case. It should be noted however that when the brace load is not due to primarily lateral loads frame action might not occur. As mentioned earlier the slip-critical strength criterion in used.
Since all of the bolts are subjected to tension simultaneously, there is interaction between tension and shear.
The reduced tensile capacity is Prying action is now checked using the method and notation of the AISC Manual of Steel Construction , pages through Check 1. Since 3. These will not control in this case.
The following method can be used when tf and tp are of similar thicknesses. Because of the axial force, the column flange can bend just as the clip angles. A yield-line analysis derived from Mann and Morris can be used to determine an effective tributary length of column flange per bolt.
The yield lines are shown in Fig. Thus, Using peff in place of p, and following the AISC procedure, Note that standard holes are used in the column flange. The method of bracing connection design presented here, the uniform force method UFM , is an equilibrium-based method. Every proper method of design for bracing connections, and in fact for every type of connection, must satisfy equilibrium. The set of forces derived from the UFM, as shown in Fig.
If it is assumed that the structure and connection behave elastically an assumption as to constitutive equations and that the beam and the column remain perpendicular to each other an assumption as to deformation—displacement equations , then an estimate of the moment in the beam due to distortion of the frame frame action Thornton, is given by With and This moment MD is only an estimate of the actual moment that will exist between the beam and column.
The actual moment will depend on the strength of the beam-to-column connection. The strength of the beam-to-column connection can be assessed by considering the forces induced in the connection by the moment MD as shown in Fig. The distortional force FD is assumed to act as shown through the gusset edge connection centroids. If the brace force P is a tension, the angle between the beam and column tends to decrease, compressing the gusset between them, so FD is a compression. If the brace force P is a compression, the angle between the beam and column tends to increase and FD is a tension.
For the elastic case with no angular distortion It should be remembered that these are just estimates of the distortional forces. The actual distortional forces will be dependent also upon the strength of the connection. Compare, for instance, HD to Hc. Hc is kips tension when HD is kips compression. The strength of the connection can be determined by considering the strength of each interface, including the effects of the distortional forces.
The following interface forces can be determined from Figs. Thus, the design shown in Fig. Note also that NBC could have been set as The NBC value of kips is used to cover the case when there is no excess capacity in the beam-to-column connection.
Now, the gusset-to-beam and gusset-to-column interfaces will be checked for the redistributed loads of Fig. Gusset to Beam. Gusset stresses: 2. No ductility factor is used here because the loads include a redistribution.
Gusset to Column. This connection is ok without calculations because the loads of Fig. It has been shown that the connection is strong enough to carry the distortional forces of Fig.
In general, the entire connection could be designed for the combined UFM forces and distortional forces, as shown in Fig. This set of forces is also admissible.
The UFM forces are admissible because they are in equilibrium with the applied forces. The distortional forces are in equilibrium with zero external forces. Under each set of forces, the parts of the connection are also in equilibrium. Therefore, the sum of the two loadings is admissible because each individual loading is admissible. A safe design is thus guaranteed by the lower bound theorem of limit analysis.
The difficulty is in determining the distortional forces. The elastic distortional forces could be used, but they are only an estimate of the true distortional forces. The distortional forces depend as much on the properties of the connection, which are inherently inelastic and affect the maintenance of the angle between the members, as on the properties and lengths of the members of the frame.
The UFM produces a load path that is consistent with the gusset plate boundaries. For instance, if the gusset-to-column connection is to a column web, no horizontal force is directed perpendicular to the column web because unless it is stiffened, the web will not be able to sustain this force. This is clearly shown in the physical test results of Gross where it was reported that bracing connections to column webs were unable to mobilize the column weak axis stiffness because of web flexibility.
A mistake that is often made in connection design is to assume a load path for a part of the connection, and then to fail to follow through to make the assumed load path capable of carrying the loads satisfying the limit states.
Note that load paths include not just connection elements, but also the members to which they are attached. As an example, consider the connection of Fig. This is a configuration similar to that of Fig. This will be called the L weld method, and is similar to model 4, the parallel force method, which is discussed by Thornton In the example of Fig.
This results in free-body diagrams for the gusset, beam, and column as shown in Fig. Imagine how difficult it would be to obtain the forces on the free-body diagram of the gusset and other members if the weld were not uniformly loaded! Every inch of the weld would have a force of different magnitude and direction. Note that while the gusset is in equilibrium under the parallel forces alone, the beam and the column require the moments as shown to provide equilibrium.
For comparison, the free-body diagrams for the UFM are given in Fig. These forces are always easy to obtain and no moments are required in the beam or column to satisfy equilibrium. While the L weld method weld is very small, as expected with this method, now consider the load paths through the rest of the connection. The column web sees a transverse force of 80 kips. It should be noted that the yield-line pattern of Fig. That analysis assumed double curvature with a prying force at the toes of the end plate a distance a from the bolt lines.
But the column web will bend away as shown in Fig. Thus, single curvature bending in the end plate must be assumed, and the required end plate thickness is given by AISC The weld is already designed. The beam must be checked for web yield and crippling, and web shear. The kip vertical load between the gusset and the beam flange is transmitted to the beam-to-column connection by the beam web.
The doubler must start at a distance x from the toe, where 4. Therefore, a doubler of length 34 — The doubler thickness td required is 1. If some yielding before ultimate load is reached is acceptable, grade 36 plate can be used. Beam to Column. The fourth connection interface the first interface is the brace-to-gusset connection, not considered here , the beam-to-column, is the most heavily loaded of them all.
The 80 kips horizontal between the gusset and column must be brought back into the beam through this connection to make up the beam strut load of kips axial. This connection also sees the kips vertical load from the gusset-to-beam connection. The reduced tension design strength is so use kips. If stiffeners are used, the most highly loaded one will carry the equivalent tension load of three bolts or The shear in the stiffener is Weld of Stiffener to Column Web. Assume about 3 in of weld at each gage line is effective, that is 1.
The load kips. The length of the weld is Additional Discussion. The kip horizontal force between the gusset and the column must be transferred to the beam-to-column connections. Therefore, the column section must be capable of making this transfer.
These couples could act on the gusset-to-column and gusset-to-beam interfaces, since they are free vectors, but this would totally change these connections. This will greatly reduce its capacity to carry kips in compression and is probably not acceptable.
This completes the design of the connection by the L weld method. The final connection as shown in Fig. The column stiffeners are expensive, and also compromise any connections to the opposite side of the column web. The web-doubler plate is an expensive detail and involves welding in the beam k-line area, which may be prone to cracking AISC, Finally, although the connection is satisfactory, its internal admissible force distribution that satisfies equilibrium requires generally unacceptable couples in the members framed by the connection.
As a comparison, consider the design that is achieved by the UFM. The statically admissible force distribution for this connection is given in Fig.
Note that all elements gusset, beam, and column are in equilibrium with no couples. Note also how easily these internal forces are computed. The final design for this method, which can be verified by the reader, is shown in Fig.
There is no question that this connection is less expensive than its L weld counterpart in Fig. As a final comment, a load path assumed for part of a connection affects every other part of the connection, including the members that frame to the connection.
All of the bracing connection examples presented here have involved connections to the column using end plates or double clips, or are direct welded. The UFM is not limited to these attachment methods.
Figures 2. These connections are much easier to erect than the double-angle or shear plate type because the beams can be brought into place laterally and easily pinned. For the column web connection of Fig. The connections shown were used on an actual job and were designed for the tensile strength of the brace to resist seismic loads in a ductile manner.
The UFM can be easily generalized to this case as shown in Fig. It should be noted that this non-concentric force distribution is consistent with the findings of Richard , who found very little effect on the force distribution in the connection when the work point is moved from concentric to non-concentric locations.
In the case of Fig. In the case of a connection to a column web, this will be the actual distribution Gross, , unless the connection to the column mobilizes the flanges, as for instance is done in Fig. An alternate analysis, where the joint is considered rigid, that is, a connection to a column flange, the moment M is distributed to the beam and column in accordance with their stiffnesses the brace is usually assumed to remain an axial force member and so is not included in the moment distribution , can be performed.
Example Consider the connection of Sec. Using the data of Fig. This figure also shows the original UFM forces of Fig. The design of this connection will proceed in the same manner as shown in Sec. The UFM as originally formulated can be applied to trusses as well as to bracing connections. After all, a vertical bracing system is just a truss as seen in Fig.
But bracing systems generally involve orthogonal members, whereas trusses, especially roof trusses, often have a sloping top chord. In order to handle this situation, the UFM has been generalized as shown in Fig.
This can always be arranged when designing a connection, but in checking a given connection designed by some other method, the constraint may not be satisfied. The result is gusset edge couples, which must be considered in the design. As an application of the UFM to a truss, consider the situation of Fig. This is a top chord connection in a large aircraft hangar structure. The truss is cantilevered from a core support area.
Thus, the top chord is in tension. The design shown in Fig. The KISS method is the simplest admissible design method for truss and bracing connections. On the negative side, however, it generates large, expensive, and unsightly connections. The problem with the KISS method is the couples required on the gusset edges to satisfy equilibrium of all parts. In the Fig. The couples 15, kips-in on the top edge and kips-in on the vertical edge are necessary for equilibrium of the gusset, top chord, and truss vertical, with the latter two experiencing only axial forces away from the connection.
Couples still result, but are much smaller than in Fig. This design is much improved over that of Fig. When the UFM of Fig. The designs of Figs. For instance, the design of Fig. The lower bound theorem of limit analysis provides an answer. This theorem basically says that for a given connection configuration, that is, Figs. As a converse to this, for a given load, the smallest connection satisfying the limit states is closest to the true required connection. Of the three admissible force distributions given in Figs.
To demonstrate the calculations required to design the connections of Figs. The geometry of Fig. First, the brace-to-gusset connection is designed, and this establishes the minimum size of gusset. For calculations for this part of the connection, see Sec. Normally, the gusset is squared off as shown in Fig. Starting from the configuration of Fig. It will be found that Fig. Therefore, the number of rows of bolts in the gusset-to-truss vertical is sequentially reduced until failure occurs.
The last-achieved successful design is the final design as shown in Fig. The calculations for Fig. For the configuration of Fig. Then, From Fig. Since , there will be a couple on this edge unless the gusset geometry is adjusted to make. In this case, we will leave the gusset geometry unchanged and work with the couple on gusset-to-top chord interface.
Of the two possible choices, the first is the better one because the rigidity of the gusset-to-top chord interface is much greater than that of the gusset-to-truss vertical interface. This is so because the gusset is direct welded to the center of the top chord flange and is backed up by the chord web, whereas the gusset- to-truss vertical involves a flexible end plate and the bending flexibility of the flange of the truss vertical.
Thus, any couple required to put the gusset in equilibrium will tend to migrate to the stiffer gusset-to-top chord interface. Gusset to top chord.
Weld: Weld length is 70 in. Gusset stress: c. The contact length N is 70 in. For convenience, an equivalent normal force acting over the contact length N can be defined as NC,equiv.
Additionally, the restraint provided by the beam end connection is sufficient to justify the check away from the end of the beam. The checks for web yield and crippling could have been dismissed by inspection in this case, but were completed to illustrate the method.
Now consider for contrast, the couple of 15, kips-in shown in Fig. Gusset to truss vertical: a. Weld: Fillet weld size required Because of the flexibility of the end plate and truss vertical flange, there is no need to size the weld to provide ductility.
The tension force will reduce the clamping force and therefore the slip resistance. Connection shear is carried by the faying surface through friction until slip occurs. Once slip occurs, the connection will behave as a bearing connection and should be checked in this manner. The truss vertical flange is therefore, ok by inspection, but a calculation will be performed to demonstrate how the flange can be checked. A formula Mann and Morris, for an effective bolt pitch can be derived from yield-line analysis as where the terms are as previously defined in Fig.
Truss vertical-to-top chord connection: The forces on this connection, from Figs. Weld: Use a profile fillet weld of the cap plate to the truss vertical, but only the weld to the web of the vertical is effective because there are no stiffeners between the flanges of the top chord.
For welds of size W on both sides of a web of thickness tw 1. Cap plate: The cap plate thickness will be governed by bearing. This completes the calculations required to produce the connection of Fig. The three main parts are joined by two additional parts, the bolts of the angles to the piece W16 and the bolts from the piece W16 to the W The load path in this connection is unique.
The load P passes from the angles through the bolts into the piece W16, thence through bolts again into the supporting W The latter bolt group is arranged to straddle the brace line of action. These bolts then see only direct tension and shear, and no additional tension due to moment. Statics is sufficient to establish this. Consider now the determination of the capacity of this connection.
Angles: The limit states for the angles are gross tension, net tension, block shear rupture, and bearing. The load can be compression as well as tension in this example. Compression will affect the angle design, but tension will control the above limit states. Gross tension: The gross area Agt is 1. Block shear rupture: This failure mode involves the tearing out of the cross-hatched block in Fig. The failure is by yield on the longitudinal line through the bolts line ab and a simultaneous fracture failure on the perpendicular line from the bolts longitudinal line to the angle toe line bc.
In this case, Ubs is taken as 0. In the present case, the force distribution is essentially uniform because the angle gage line and the angle gravity axis are close to each other. The procedure is as follows for each bolt. For the upper bolt, the limit states are 1.
For the lower bolt, the limit states are 1. Bolts—angles to piece W The limit state for the bolts is shear. In this case, the bolts are in double shear and the double shear value per bolt is Note that because of bearing limitations, this value cannot be achieved.
Because there is only one line of bolts, block shear is not a limit state. Bearing has already been considered with the angle checks. Whitmore section: This is the section denoted by lw on Fig. If the load P is a compression, it is possible for the gusset to buckle laterally in a sidesway mode. For this mode of buckling, the K factor is 1. Thus, from Section E3, b.
Bearing: This has been considered with the angles, above. Prying action: Prying action explicitly refers to the extra tensile force in bolts that connect flexible plates or flanges subjected to loads normal to the flanges. For this reason, prying action involves not only the bolts but the flange thickness, bolt pitch and gage, and in general, the geometry of the entire connection.
This method was originally developed by Struik and deBack and presented in the book Kulak et al. The form used in the AISC LRFD Manual was developed by Thornton , for ease of calculation and to provide optimum results, that is, maximum capacity for a given connection analysis and minimum required thickness for a given load design.
Thornton , has shown that this method gives a very conservative estimate of ultimate load and shows that very close estimates of ultimate load can be obtained by using the flange ultimate strength, Fu, in place of yield strength, Fy, in the prying action formulas. Note that the resistance factor, f, used with the Fu is 0. From the foregoing calculations, the capacity design strength of this connection is Let us take this as the design load required strength and proceed to the prying calculations.
The vertical component of Note that the bolts also need to be checked for bearing as was done for the angles.
The bolts will not be critical, that is, the bolts will not limit the prying strength. A method for doing this was presented in Fig. Thus, Now, using the prying formulation from the AISC Manual, Note that the prying lever arm is controlled by the narrower of the two flanges. This completes the design calculations for this connection. A load path has been provided through every element of the connection.
For this type of connection, the beam designer should make sure that the bottom flange is stabilized if P can be compressive. A transverse beam framing nearby as shown in Fig. The area of the pier that is concentric with A1 is A2. If the pier is not concentric with the base plate, only the portion that is concentric can be used for A2. The formulation given here was developed by Thornton a, b based on previous work by Murray , Fling , and Stockwell Example The column of Fig.
The concrete has ksi. Try a base plate of A36 steel, 4 in bigger than the column in both directions. Erection Considerations. In addition to designing a base plate for the column compression load, loads on base plates and anchor rods during erection should be considered. The latest OSHA requirements postulate a lb. Note these loads would be applied sequentially. A common design load for erection, which is much more stringent than the OSHA load, is a 1-kip working load, applied at the top of the column in any horizontal direction.
If the column is, say, 40 ft high, this 1- kip force at a lever arm of 40 ft will cause a significant couple at the base plate and anchor bolts. The base plate, anchor bolts, and column-to-base plate weld should be checked for this construction load condition. The paper by Murray gives some yield-line methods that can be used for doing this. This is an OSHA erection requirement for all columns except minor posts.
These splices are nominal in the sense that they are designed for no particular loads. Section J1. Column Splices. If the column load remains compression, the strong-axis column shear can be carried by friction.
The coefficient of static friction of steel to steel is on the order of 0. Suppose the compression load on this column is kips. How much major axis bending moment can this splice carry? Even though these splices are nominal, they can carry quite significant bending moment. In order for a bending moment to cause a tension in the column flange, this load of kips must first be unloaded. The splice plates and bolts will allow additional moment to be carried.
It can be shown that the controlling limit state for the splice material is bolt shear. The splice forces are assumed to act at the faying surface of the deeper member. The total moment capacity of this splice with zero compression is thus The role of compression in providing moment capability is often overlooked in column splice design.
Erection Stability. As discussed earlier for base plates, the stability of columns during erection must be a consideration for splice design also. The usual nominal erection load for columns is a 1-kip horizontal force at the column top in any direction. In LRFD format, the 1-kip working load is converted to a factored load by multiplying by a load factor of 1. It has been established that for major axis bending, the splice is good for This means that the 1.
Most columns will be shorter than Minor Axis Stability. If the 1. The upper shaft will tend to pivot about point O. Errors can be avoided by making all column gages the same. If the upper column of Fig. If it were not, larger or stronger bolts could be used. The simplest method for designing this type of splice is to establish a flange force required strength that is statically equivalent to the applied moments and then to design the bolts, welds, plates, and fillers if required for this force.
Major Axis Bending. If Mx is the major axis applied moment and d is the depth of the deeper of the two columns, the flange force or required strength is Minor Axis Bending. The force distribution is similar to that shown in Fig. The force F in the case of actual factored design loads can be quite large and will need to be distributed over some finite bearing area as shown in Fig. In Fig. The quantities T and F are for each of the two flanges.
The bearing area is determined by requiring that the bearing stress reaches its design strength at the load F. Thus, 0. The completed splice is shown in Fig. Since the columns are of different depths, fill plates will be needed. Since this splice is a bearing splice, either the fills must be developed, or the shear strength of the bolts must be reduced.
Next, the splice plates are designed. These plates will be approximately as wide as the narrower column flange. As discussed earlier, these splices may be positioned in the center of a truss panel and, therefore, must provide some degree of continuity to resist bending. For the tension chord, the splice must be designed to carry the full tensile load.
Example Design the tension chord splice shown in Fig. The load is kips factored. The web load path is similar. Flange connection. Member limit states: a. Bolts: Although not a member limit state, a bolt pattern is required to check the chords. Try 6 bolts in 2 rows of 3 as shown in Fig. Assume that there will be two web holes in alignment with the flange holes. Block shear fracture: 2. Flange plates: Since the bolts are assumed to be in double shear, the load path is such that one half of the flange load goes into the outer plate, and one half goes into the inner plates.
The gross area in tension required is and the thickness required is 4. The gross area in tension required is Try a plate 4 in wide.
Then the required thickness is 2. The plate will fail in net tension. This completes the calculation for the flange portion of the splice.
The bolts, outer plate, and inner plates, as chosen above, are ok. Web connection: The calculations for the web connection involve the same limit states as the flange connection, except for chord net section, which involves flanges and web. Bolts: A bolt pattern is required to check the web. Try four bolts. Block shear fracture: Assume the bolts have a 3-in pitch longitudinally.
Since the block shear limit state fails, the bolts can be spaced out to increase the capacity. Increase the bolt pitch from the 3 in assumed above to 6 in. Then The web bolt pattern shown in Fig. At this point, there are four bolts in the web at 6-in pitch, but the six bolts shown will be required.
Net area will be ok by inspection. Block shear rupture: This is checked as shown in previous calculations. It is not critical here. Bolt shear: b. The 6-in pitch become 3-in pitch as shown in Fig. Tearout between bolts is still not critical. Additional checks because of change in web bolts pattern: a. The final design is shown in Fig.
If this were a non-bearing compression splice, the splice plates would be checked for buckling. The following paragraph shows the method, which is not required for a tension splice. This has already been done. This limit state is checked for the flange plates also. Additional views are shown in Figs.
If the strong axis connection requires stiffeners, there will be an interaction between the flange forces of the strong and weak axis beams. Alternative actions should be considered for the design of bridges. BS EN [7] gives design guidance and values of actions to be used when designing buildings and civil engineering works.
It contains guidance on:. The accompanying UK National Annex [8] presents tables containing significantly more occupancy sub-groups than given in the main text of the Eurocode. Some typical values are given in the tables below. The methods given in BS EN [9] should be used to determine the thermal and mechanical actions that act on structures exposed to fire.
The values of actions determined should be used when carrying out fire engineering design to Part of the relevant material Eurocode. The values of actions determined are considered to be accidental actions.
The UK NA [10] gives guidance for temperature analysis and fire models. For the period of time within which to make the temperature analysis the UK NA [10] refers the designer to the:. BS EN [11] gives roof snow load coefficients that are to be used with the characteristic ground snow load maps given in Annex C of that Part of BS EN to determine design roof snow loads for different roof shapes.
The UK National Annex [12] replaces the ground snow load map and some of the roof coefficients for buildings to be constructed in the UK. The guidance given in BS EN [13] should be used to determine the wind actions to be considered during the structural design of buildings and civil engineering works.
The information given is applicable to the whole or part of a structure, including elements attached to it such as cladding. The values of wind actions are derived from a fundamental value of the basic wind velocity which is given in the appropriate National Annex , from which a mean wind speed and peak velocity pressure are determined for the particular building; wind pressures and forces are determined using coefficients given in BS EN [13].
Guidance to assist structural engineers with the evaluation of wind actions for buildings in the UK is available in SCI-P, and a Wind loading calculator is also available. Where structures are exposed to daily and seasonal climatic changes in temperature, the effects of thermal actions should be accounted for in the design. BS EN [15] gives principles and general rules that should be used to determine the characteristic values of thermal actions.
The values of actions which should be taken into account during the construction of a building or civil engineering works should be obtained from the principles and general rules given in BS EN [16].
The SCI advisory desk note AD gives guidance for determining the value of the actions present during the execution of a steel and concrete composite floor. Strategies and rules for safeguarding buildings and other civil engineering works against accidental actions are given in BS EN [17]. There are no rules for determining specific values of accidental actions caused by external explosions, warfare or terrorist activities, or for verifying the residual stability of structures damaged by seismic action or fire, etc.
Information regarding limiting the effects of a localised failure in buildings from an unspecified cause is given in Annex A of BS EN [17]. The effects are limited in order to avoid disproportionate collapse of the structure.
Annex A includes information relating to:. BS EN [33] Eurocode 3: Design of steel structures comprises a set of general rules in twelve parts BS EN [20] to BS EN [27] for all types of steel structure and additional rules in separate Parts for structures other than buildings, e. BS EN [28] for bridges. When designing a building structure of rolled sections and plate girders, the following parts of BS EN [33] will be required. For steel and concrete composite structures, Eurocode 3 is referred to by Eurocode 4 [34] for the design of the steel elements.
These cover all the essential rules for steel building design in accordance with the UK National Annexes. BS EN [20] gives generic design rules for steel structures and specific guidance for structural steelwork used in buildings. The main aspects in BS EN [20] are:. In exceptional circumstances, components might use higher strength grades; BS EN [27] gives guidance on the use of higher strength steels.
For the design of stainless steel components and structures, reference should be made to BS EN [23]. The UK National Annex [21] states that the nominal yield strength f y and ultimate strength f u of steel should be obtained from the minimum specified values according to the product standards.
Material requirements for fasteners bolts are given in BS EN [25]. Section 5. Generally, first order elastic global analysis may be used. In some circumstances depending on member classification plastic global analysis may be used. Where the internal moments and forces are significantly increased due to deflections, second order effects need to be taken into account, either through magnification of first order effects or by a second order analysis.
Extract from Table 5. Four classes of cross section are defined in BS EN [20]. Each part of a section that is in compression is classified and the class of the whole cross section is deemed to be the highest least favourable class of its compression parts. Table 5. Expressions for determining the cross section resistance in tension, compression, bending and shear for the four classes of sections are given in Section 6.
Section 6 also provides rules for the verification of cross-sections subject to combined effects such as shear and bending.
For slender webs, the shear resistance may be limited by shear buckling; for such situations, reference is made to BS EN [24] Shear buckling is rarely a consideration with hot rolled sections.
The choice of curve depends on the type of cross-section, and the axis about which buckling will take place. Different curves are used for different buckling modes as explained in SCI P BS EN [20] presents guidance for checking flexural, torsional and torsional-flexural buckling for members in compression.
The latter two modes will not be critical for doubly symmetric I or H sections, or hollow sections. Laterally unrestrained members in bending about their major axes need to be verified against lateral torsional buckling. Rules are given in Clause 6. The guidance given for calculating the beam slenderness for the first two approaches requires the value of the elastic critical moment for lateral torsional buckling M cr , but no expressions are given for determining this value.
An on-line calculator is also available. The third method treats the compression flange and part of the web as a simple compression member. For members subject to bending and axial compression, the criteria given in 6.
Interaction factors k ij used in the verifications may be calculated using either method 1 or 2 given respectively in Annexes A or B of BS EN [20]. Method 2 is considered to be the simpler of the two methods and is recommended for use in the UK.
The general method given in 6. The general method gives guidance for structural components that are not covered by the guidance given for compression, bending or bending and axial compression members, and is not likely to be used by most building designers. BS EN [20] does not give any serviceability limit state limits for dynamic effects, vertical deflections and horizontal deflections. The National Annex for the country where the building is to be constructed should be consulted for guidance.
The UK National Annex [21] gives limits for deflections; limits for specific projects should be agreed with the client if they differ from the proposed limits. Informative Annex BB of EN [20] gives guidance for buckling of structural components in buildings. Guidance is given for:. The provisions of BS EN [24] are mainly appropriate to the design of plate girders, where the elements of the cross section are typically more slender.
For building frames using hot rolled sections, there is little need to refer to this Part, except for the design of webs subject to transverse forces due to concentrated local forces commonly referred to as the determination of web bearing and buckling resistances.
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