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Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Momen...
Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.1 Introduction: If gravity loads are applied to a fairly long, simply supported beam, the beam will bend downward, and its upper part will be placed in compression and will act as a compression member. The cross section of this “column” will consist of the portion of the beam cross section above the neutral axis. For the usual beam, the “column” will have a much smaller moment of inertia about its y or vertical axis than about its x axis. 1 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.1 Introduction: If nothing is done to brace it perpendicular to the y axis, it will buckle laterally at a much smaller load than would otherwise have been required to produce a vertical failure. Lateral buckling will not occur if the compression flange of a member is braced laterally or if twisting of the beam is prevented at frequent intervals. In this chapter, we will look at beams as follows: 1. First, the beams will be assumed to have continuous lateral bracing for their compression flanges. 2. Next, the beams will be assumed to be braced laterally at short intervals. 3. Finally, the beams will be assumed to be braced laterally at larger and larger intervals. 2 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.1 Introduction: Fig. 9.1 shows that beams have three distinct zones of behavior, depending on their lateral bracing situation. If we have continuous or closely spaced lateral bracing, the beams will experience yielding of the entire cross section and fall into what is classified as Zone 1. As the distance between lateral bracing is increased further, the beams will begin to fail inelastically at smaller moments and fall into Zone 2. Finally, with even larger unbraced lengths, the beams will fail elastically and fall into Zone 3. 3 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.1 Introduction: Fig.(9.1): Nominal moment as function of unbraced length of compression Flange. 4 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.1.1 Plastic Behavior (Zone 1): If we take a compact beam whose compression flange is continuously braced laterally, we would find that we could load it until its full plastic moment 𝑴𝒑 is reached at some point or points; further loading then produces a redistribution of moments, as was described in Chapter 8. In other words, the 𝑴𝒑 moments in these beams can reach and then develop a rotation capacity sufficient for moment redistribution. If we now take one of these compact beams and provide closely spaced intermittent lateral bracing for its compression flanges, we will find that we can still load it until the plastic moment plus moment redistribution is achieved if the spacing between the bracing does not exceed a certain value, called 𝑳𝒑 herein. (The value of 𝑳𝒑 is dependent on the dimensions of the beam cross section and on its yield stress). 5 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.1.2 Inelastic Buckling (Zone 2): If we now further increase the spacing between points of lateral or torsional bracing, the section may be loaded until some, but not all, of the compression fibers are stressed to Fy. The section will have insufficient rotation capacity to permit full moment redistribution and thus will not permit plastic analysis. In other words, in this zone we can bend the member until the yield strain is reached in some, but not all, of its compression elements before lateral buckling occurs. This is referred to as inelastic buckling. As we increase the unbraced length, we will find that the moment the section resists will decrease, until finally it will buckle before the yield stress is reached anywhere in the cross section. The maximum unbraced length at which we can still reach Fy at one point is the end of the inelastic range. It’s shown as 𝑳𝒓 in Fig. 9.1; its value is dependent upon the properties of the beam cross section, as well as on the yield and residual stresses of the beam. 6 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.1.3 Elastic Buckling (Zone 3): If the unbraced length 𝑳𝒓 is greater than the section will buckle elastically before the yield stress is reached anywhere. As the unbraced length is further increased, the buckling moment becomes smaller and smaller. As the moment is increased in such a beam, the beam will deflect more and more transversely until a critical moment value 𝑴𝒄𝒓 is reached. At this time, the beam cross section will twist and the compression flange will move laterally. The moment 𝑴𝒄𝒓 is provided by the torsional resistance and the warping resistance of the beam. 7 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.2. FULL PLASTIC MOMENT (ZONE 1): 8 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.3. DESIGN OF BEAMS (ZONE 1): Included in the items that need to be considered in beam design are moments, shears, deflections, crippling, lateral bracing for the compression flanges, fatigue, and others. Beams will probably be selected that provide sufficient design moment capacities (Φb Mn) and then checked to see if any of the other items are critical. The factored moment will be computed, and a section having that much design moment capacity will be initially selected from the AISC Manual, Part 3, Table 3‐2, entitled “W Shapes Selection by 𝒁𝒙 ”. From this table, steel shapes having sufficient plastic moduli to resist certain moments can quickly be selected. Two important items should be remembered in selecting shapes: 9 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.3. DESIGN OF BEAMS (ZONE 1): 1. These steel sections cost so many cents per pound, and it is therefore desirable to select the lightest possible shape having the required plastic modulus (assuming that the resulting section is one that will reasonably fit into the structure). The table has the sections arranged in various groups having certain ranges of plastic moduli. The heavily typed section at the top of each group is the lightest section in that group, and the others are arranged successively in the order of their plastic moduli. Normally, the deeper sections will have the lightest weights giving the required plastic moduli, and they will be generally selected, unless their depth causes a problem in obtaining the desired headroom, in which case a shallower but heavier section will be selected. 10 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.3. DESIGN OF BEAMS (ZONE 1): 2. The plastic moduli values in the table are given about the horizontal axes for beams in their upright positions. If a beam is to be turned on its side, the proper plastic modulus about the y axis can be found in Table 3‐4 of the Manual or in the tables giving dimensions and properties of shapes in Part 1 of the AISC Manual. A W shape turned on its side may be only from 10 to 30 percent as strong as one in the upright position when subjected to gravity loads. 11 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments Example 9‐1: 12 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments Example 9‐1: 13 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments Example 9‐2: 14 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments Example 9‐2: 15 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments Example 9‐2: Select Beam Section: 16 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments Example 9‐3: 17 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments Example 9‐3: Solution: 18 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 8 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.4 Lateral Support Of Beams: Many steel beams are used in such a manner that their compression flanges are restrained against lateral buckling. Beams used to support concrete building and bridge floors are often incorporated in these concrete floors. For situations of this type, the beams will fall into Zone 1. If the compression flange of a beam be without lateral support for some distance, it will have a stress situation similar to that existing in columns. When the compression flange of a beam is long enough and slender enough, it may quite possibly buckle, unless lateral support is provided. There are many factors affecting the amount of stress that will cause buckling in the compression flange of a beam such as the properties of the material, the spacing and types of lateral support provided, residual stresses in the sections, the types of end support or restraints, the loading conditions, etc. 1 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.4 Lateral Support Of Beams: 2 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.4 Lateral Support Of Beams: The tension in the other flange of a beam tends to keep that flange straight and restrain the compression flange from buckling; but as the bending moment is increased, the tendency of the compression flange to buckle may become large enough to overcome the tensile restraint. When the compression flange does begin to buckle, twisting or torsion will occur, and the smaller the torsional strength of the beam the more rapid will be the failure. The W, S, and channel shapes so frequently used for beam sections do not have a great deal of resistance to lateral buckling and the resulting torsion. Some other shapes, the built‐up box shapes are stronger. These types of members have a great deal more torsional resistance than the W, S, and plate girder sections. 3 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.4 Lateral Support Of Beams: 4 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.4 Lateral Support Of Beams: Some judgment needs to be used in deciding what does and what does not constitute satisfactory lateral support for a steel beam. A beam that is wholly encased in concrete or that has its compression flange incorporated in a concrete slab is certainly well supported laterally. However, when a concrete slab rests on the top flange of a beam, the engineer must study the situation carefully before he counts on friction to provide full lateral support. If the loads on the slab are fairly well fixed in position, they will contribute to the friction and it may be reasonable to assume full lateral support. If, on the other hand, there is much movement of the loads and appreciable vibration, the friction may well be reduced and full lateral support cannot be assumed. Such situations occur in bridges due to traffic, and in buildings with vibrating machinery such as printing presses. 5 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.4 Lateral Support Of Beams: If lateral support of the compression flange not be provided by a floor slab, it is possible that such support may be provided with connecting beams or with special members inserted for that purpose. Beams that frame into the sides of the beam or girder in question and are connected to the compression flange can usually be counted on to provide full lateral support at the connection. However, if the connection is made primarily to the tensile flange, little lateral support is provided to the compression flange. Before support is assumed from these beams, the designer should note whether the beams themselves are prevented from moving. The beams represented with horizontal dashed lines in Fig. 9.7 provide questionable lateral support for the main beams between columns. 6 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.4 Lateral Support Of Beams: For a situation of this type, some system of x‐bracing may be desirable in one of the bays. Such a system is shown in Fig. 9.7. This one system will provide sufficient lateral support for the beams for several bays. 7 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.4 Lateral Support Of Beams: The intermittent welding of metal roof or floor decks to the compression flanges of beams will probably provide sufficient lateral bracing. If there be doubt in the designer’s mind as to the degree of lateral support provided, he should probably be advised to assume that there is none. 8 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.4 Lateral Support Of Beams: 9 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.5 Introduction into Inelastic Buckling (Zone2): If intermittent lateral bracing is supplied for the compression flange of a beam section, or if intermittent torsional bracing is supplied to prevent twisting of the cross section at some (but not all) of its compression elements before lateral buckling occurs, we have inelastic buckling. In other words, the bracing is insufficient to permit the member to reach a full plastic strain distribution before buckling occurs. 10 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.5.1 Bending Coefficients : In the formulas presented in the next few sections for inelastic and elastic buckling, we will use a term (Cb) called the lateral‐torsional buckling modification factor for nonuniform moment diagrams, when both ends of the unsupported segment are braced. This is a moment coefficient that is included in the formulas to account for the effect of different moment gradients on lateral‐torsional buckling. In other words, lateral buckling may be appreciably affected by the end restraint and loading conditions of the member. As an illustration, the moment in the unbraced beam of part (a) of Fig. 9.8 causes a worse compression flange situation than does the moment in the unbraced beam of part (b). For one reason, the upper flange of the beam in part (a) is in compression for its entire length, while in (b) the length of the upper flange that is in compression is much less. 11 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.5.1 Bending Coefficients : The basic moment capacity equations for Zones 2 and 3 were developed for laterally unbraced beams subject to single curvature, with Frequently, beams are not bent in single curvature, with the result that they can resist more moment. We have seen this in Fig. 9.8. Cb = 1.14 Cb = 2.38 12 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.5.1 Bending Coefficients : To handle this situation, the AISC Specification provides moment or Cb coefficients larger than 1.0 that are to be multiplied by the computed Mn values. The results are higher moment capacities. When using Cb values, the designer should clearly understand that the moment capacity obtained by multiplying Mn by Cb may not be larger than the plastic Mn of Zone 1, which is Mp and is equal to Fy Z. This situation is illustrated in Fig. 9.9. 13 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.5.1 Bending Coefficients : FIGURE 9.9 14 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.5.1 Bending Coefficients : The value of Cb for singly symmetric members in single curvature and all doubly symmetric members is determined from the expression to follow, in which Mmax is the largest moment in an unbraced segment of a beam, while MA , MB , and MC are, respectively, the moments at the 1/4 point, 1/2 point, and 3/4 point in the segment: Cb = 12.5 Mmax (AISC Equation F1‐1) 2.5 Mmax + 3MA + 4MB + 3MC Cb is equal to 1.0 for cantilevers or overhangs where the free end is unbraced. Some typical values of Cb, calculated with the previous AISC Equation F1‐1, are shown in Fig. 9.10 for various beam and moment situations. Some of these values are also given in Table 3‐1 of the AISC Manual. 15 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.5.1 Bending Coefficients : 16 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.5.1 Bending Coefficients : 17 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.5.1 Bending Coefficients : Cb =1.14 18 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.5.1 Bending Coefficients : Cb = 2.38 19 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.6 MOMENT CAPACITIES (ZONE 2) : The nominal moment strengths for unbraced lengths between Lp and Lr are calculated with the equation to follow: Lr is a function of several of the section’s properties, such as its cross‐sectional area, modulus of elasticity, yield stress, and warping and torsional properties. The very complex formulas needed for its computation are given in the AISC Specification (F1). Fortunately, numerical values have been determined for sections normally used as beams and are given in AISC Manual Table 3‐2, entitled “W Shapes Selected by Zx.” 20 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.6 MOMENT CAPACITIES (ZONE 2) : The interpolation expressions that follow are presented on page 3‐10 of the AISC Manual. The bending factors (BFs) represent part of AISC Equation F2‐2, as can be seen by comparing the equations to follow with that equation. Their numerical values in kips are given in Manual Table 3‐2 for W shapes. 21 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.6 MOMENT CAPACITIES (ZONE 2) : 22 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.6 MOMENT CAPACITIES (ZONE 2) : 23 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.7 ELASTIC BUCKLING (ZONE 3) and MOMENT CAPACITIES : If the unbraced length of a beam is greater than Lr , the beam will fall in Zone 3. Such a member may fail due to buckling of the compression portion of the cross section laterally about the weaker axis, with twisting of the entire cross section about the beam’s longitudinal axis between the points of lateral bracing. This will occur even though the beam is loaded so that it supposedly will bend about the stronger axis. The beam will bend initially about the stronger axis until a certain critical moment Mcr is reached. At that time, it will buckle laterally about its weaker axis. As it bends laterally, the tension in the other flange will try to keep the beam straight. As a result, the buckling of the beam will be a combination of lateral bending and a twisting (or torsion) of the beam cross section. A sketch of this situation is shown in Fig. 9.11. 24 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.7 ELASTIC BUCKLING (ZONE 3) and MOMENT CAPACITIES : Fig. 9.11 Lateral‐torsional buckling of a simply supported beam. The critical moment, or flexural‐torsional moment Mcr in a beam will be made up of the torsional resistance and the warping resistance of the section. If the unbraced length of the compression flange of a beam section or the dis‐ tance between points that prevent twisting of the entire cross section is greater than Lr, the section will buckle elastically before the yield stress is reached anywhere in the section. 25 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.7 ELASTIC BUCKLING (ZONE 3) and MOMENT CAPACITIES : In Section F2.2 of the AISC Specification, the buckling stress for doubly symmetric I‐shaped members is calculated with the following expression: Mn = FcrSx ≤ Mp (AISC Equation F2‐3) 26 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.7 ELASTIC BUCKLING (ZONE 3) and MOMENT CAPACITIES : It is not possible for lateral‐torsional buckling to occur if the moment of inertia of the section about the bending axis is equal to or less than the moment of inertia out of plane. For this reason the limit state of lateral‐torsional buckling is not applicable for shapes bent about their minor axes, for shapes with Ix ≤ Iy , or for circular or square shapes. Furthermore, yielding controls if the section is noncompact. 27 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.7 ELASTIC BUCKLING (ZONE 3) and MOMENT CAPACITIES : 28 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.8 DESIGN CHARTS OF BEAMS: The values of φb Mn and Mn/Ωb for sections normally used as beams have been computed by the AISC, plotted for a wide range of unbraced lengths, and shown as Table 3‐10 in the AISC Manual. These diagrams enable us to solve any of the problems previously considered in this chapter in just a few seconds. The values provided cover unbraced lengths in the plastic range, in the inelastic range, and on into the elastic buckling range (Zones 1–3). They are plotted for Fy = 50 ksi and Cb = 1.0. The LRFD curve for a typical W section is shown in Fig. 9.12. The charts were developed without regard to such things as shear, deflection. They cover almost all of the unbraced lengths encountered in practice. 1 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.8 DESIGN CHARTS OF BEAMS: The LRFD curve for a typical W section is shown in Fig. 9.12. For each of the shapes, Lp is indicated with a solid circle ( ), while Lr is shown with a hollow circle ( ο ). If Cb is greater than 1.0, the values given will be magnified somewhat. FIGURE 9.12 LRFD design moment for a beam plotted versus unbraced length, Lb. 2 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 8 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.8 DESIGN CHARTS OF BEAMS: Figure 9‐13: 3 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 8 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.8 DESIGN CHARTS OF BEAMS: 4 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.8 DESIGN CHARTS OF BEAMS: Example 9‐8: Using 50 ksi steel, select the lightest available section for the beam of Fig. 9.14, which has lateral bracing provided for its compression flange, only at its ends. Assume that Cb = 1.00 for this example. (It’s actually 1.14.) Use both LRFD and ASD methods. 5 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.8 DESIGN CHARTS OF BEAMS: 6 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.8 DESIGN CHARTS OF BEAMS: Example 9‐9: Using 50 ksi steel and both the LRFD and ASD methods, select the lightest available section for the situation shown in Fig. 9.15. Bracing is provided only at the ends and center line of the member, and thus, Lb = 17 ft. Using Fig. 9.10, Cb is 1.67 if the only uniform load is the member self‐weight and it is neglected. If the self‐weight is considered then Cb will be between 1.67 and 1.30. Since the self‐weight is a small portion of the design moment, Cb is near the value of 1.67 and using it would be a reasonable assumption. 7 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.8 DESIGN CHARTS OF BEAMS: 8 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.8 DESIGN CHARTS OF BEAMS: 9 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.8 DESIGN CHARTS OF BEAMS: Example 9‐10: Using 50 ksi steel and both the LRFD and ASD methods, select the lightest available section for the situation shown in Fig. 9.16. Bracing is provided only at the ends and at midspan. 10 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.8 DESIGN CHARTS OF BEAMS: 11 Structural Steel Design I Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 8 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department 12 Structural Steel Design II Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.9 NONCOMPACT SECTIONS: A compact section is a section that has a sufficiently stocky profile so that it is capable of developing a fully plastic stress distribution before buckling locally (web or flange). For a section to be compact: The width thickness ratio of the flanges of W‐ or other I‐shaped rolled sections must not exceed a b/t value λp = 0.38 E/Fy. Similarly, the webs in flexural compression must not exceed an h/tw value λp = 3.76 E/Fy. The values of b, t, h, and tw are shown in Fig. 9.17. 1 Structural Steel Design II Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.9 NONCOMPACT SECTIONS: 2 Structural Steel Design II Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.9 NONCOMPACT SECTIONS: A noncompact section is one for which the yield stress can be reached in some, but not all, of its compression elements before buckling occurs. It is not capable of reaching a fully plastic stress distribution. For the noncompact range: The width thickness ratio of the flanges of W‐ or other I‐shaped rolled sections must not exceed a b/t value λr = 1.0 E/Fy. Similarly, the webs in flexural compression must not exceed an h/tw value λr = 5.70 E/Fy. The values of λp and λr provided in AISC Table B4.1b. For noncompact beams, the nominal flexural strength Mn is the lowest of the lateral‐torsional buckling strength, the compression flange local buckling strength. 3 Structural Steel Design II Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.9 NONCOMPACT SECTIONS: Fig. C‐F1.1. Nominal flexural strength vs. the flange width to thickness ratio of rolled I – shapes. 4 Structural Steel Design II Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.9 NONCOMPACT SECTIONS: Almost all of the standard hot‐rolled W, M, S, and C shapes listed in the AISC Manual are compact, and none of them fall into the slender classification. All of these shapes have compact webs, but a few of them have noncompact flanges. We particularly must be careful when working with built‐up sections as they may very well be noncompact or slender. In this section we will consider a shape which has a noncompact flange. 5 Structural Steel Design II Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.9 NONCOMPACT SECTIONS: If a standard shape has a noncompact flange, it will be indicated in the Manual with an “f” footnote. The numerical values shown in the tables are based on the reduced stresses caused by noncompactness. As indicated in AISC Specification F3 the flange of a member is noncompact if λp < λ ≤ λr and the member will buckle inelastically. These values are given for different shapes in AISC Specification Table B4.1. 6 Structural Steel Design II Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.9 NONCOMPACT SECTIONS: Example 9‐11: Determine the LRFD flexural design stress and the ASD allowable flexural stress for a 50 ksi W12 * 65 section which has full lateral bracing. 7 Structural Steel Design II Al‐Nahrain University Dr. Laith Khalid Kamil Chapter 9 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Design of Beams for Moments 9.9 NONCOMPACT SECTIONS: 8 ^ƚƌƵĐƚƵƌĂů ^ƚĞĞů ĞƐŝŐŶ // ůͲEĂŚƌĂŝŶ hŶŝǀĞƌƐŝƚLJ ƌ͘ >ĂŝƚŚ ĂŝƚŚ d^^h: d dK^, ZEd E^/KE; Z/E'ͲdzW KEE d/KE^Ϳ͗ Ϯ ^ƚƌƵĐƚƵƌĂů ^ƚĞĞů ĞƐŝŐŶ // ůͲEĂŚƌĂŝŶ hŶŝǀĞƌƐŝƚLJ ƌ͘ >ĂŝƚŚ d^^h: d dK^, ZEd E^/KE; Z/E'ͲdzW KEE d/KE^Ϳ͗ ϯ ^ƚƌƵĐƚƵƌĂů ^ƚĞĞů ĞƐŝŐŶ // ůͲEĂŚƌĂŝŶ hŶŝǀĞƌƐŝƚLJ ƌ͘ >ĂŝƚŚ d^^h: d dK^, ZEd E^/KE; Z/E'ͲdzW KEE d/KE^Ϳ͗ ϰ ^ƚƌƵĐƚƵƌĂů ^ƚĞĞů ĞƐŝŐŶ // ůͲEĂŚƌĂŝŶ hŶŝǀĞƌƐŝƚLJ ƌ͘ >ĂŝƚŚ d^^h: d dK^, ZEd E^/KE; Z/E'ͲdzW KEE d/KE^Ϳ͗ ϱ ^ƚƌƵĐƚƵƌĂů ^ƚĞĞů ĞƐŝŐŶ // ůͲEĂŚƌĂŝŶ hŶŝǀĞƌƐŝƚLJ ƌ͘ >ĂŝƚŚ d^^h: d dK^, ZEd E^/KE; Z/E'ͲdzW KEE d/KE^Ϳ͗ ϲ ^ƚƌƵĐƚƵƌĂů ^ƚĞĞů ĞƐŝŐŶ // ůͲEĂŚƌĂŝŶ hŶŝǀĞƌƐŝƚLJ ƌ͘ >ĂŝƚŚ d^^h: d dK^, ZEd E^/KE;^>/WͲZ/d/>KEE d/KE^Ϳ͗ ϳ ^ƚƌƵĐƚƵƌĂů ^ƚĞĞů ĞƐŝŐŶ // ůͲEĂŚƌĂŝŶ hŶŝǀĞƌƐŝƚLJ ƌ͘ >ĂŝƚŚ d^^h: d dK^, ZEd E^/KE;^>/WͲZ/d/>KEE d/KE^Ϳ͗ ϴ ^ƚƌƵĐƚƵƌĂů ^ƚĞĞů ĞƐŝŐŶ // ůͲEĂŚƌĂŝŶ hŶŝǀĞƌƐŝƚLJ ƌ͘ >ĂŝƚŚ d^^h: d dK^, ZEd E^/KE;^>/WͲZ/d/>KEE d/KE^Ϳ͗ ϵ ^ƚƌƵĐƚƵƌĂů ^ƚĞĞů ĞƐŝŐŶ // ůͲEĂŚƌĂŝŶ hŶŝǀĞƌƐŝƚLJ ƌ͘ >ĂŝƚŚ K^KEK>d :K/Ed^͗ ¾ ŽůƚĞĚ ĂŶĚ ƌŝǀĞƚĞĚ ĐŽŶŶĞĐƚŝŽŶƐ ƐƵďũĞĐƚĞĚ ƚŽ ƉƵƌĞ ƚĞŶƐŝůĞ ůŽĂĚƐ ŚĂǀĞ ďĞĞŶ ĂǀŽŝĚĞĚ ĂƐ ŵƵĐŚ ĂƐ ƉŽƐƐŝďůĞ ŝŶ ƚŚĞ ƉĂƐƚ ďLJ ĚĞƐŝŐŶĞƌƐ͘ dŚĞ ƵƐĞ ŽĨ ƚĞŶƐŝůĞ ĐŽŶŶĞĐƚŝŽŶƐ ǁĂƐ ƉƌŽďĂďůLJ ƵƐĞĚ ŵŽƌĞ ŽĨƚĞŶ ĨŽƌ ǁŝŶĚͲďƌĂĐŝŶŐ ƐLJƐƚĞŵƐ ŝŶ ƚĂůů ďƵŝůĚŝŶŐƐ ƚŚĂŶ ĨŽƌ ĂŶLJ ŽƚŚĞƌ ƐŝƚƵĂƚŝŽŶ͘ ¾ KƚŚĞƌ ůŽĐĂƚŝŽŶƐ ĞdžŝƐƚ͕ ŚŽǁĞǀĞƌ͕ ǁŚĞƌĞ ƚŚĞLJ ŚĂǀĞ ďĞĞŶ ƵƐĞĚ͕ ƐƵĐŚ ĂƐ ŚĂŶŐĞƌ ĐŽŶŶĞĐƚŝŽŶƐ ĨŽƌ ďƌŝĚŐĞƐ͕ ĨůĂŶŐĞ ĐŽŶŶĞĐƚŝŽŶ ĨŽƌ ƉŝƉŝŶŐ ),*85( +DQJHUFRQQHFWLRQ ƐLJƐƚĞŵƐ͕ ĞƚĐ͘ &ŝŐƵƌĞ ϭϯ͘ϭϱ ƐŚŽǁƐ Ă ŚĂŶŐĞƌͲƚLJƉĞ ĐŽŶŶĞĐƚŝŽŶ ǁŝƚŚ ĂŶ ĂƉƉůŝĞĚ ƚĞŶƐŝůĞ ůŽĂĚ͘ ϭϬ ^ƚƌƵĐƚƵƌĂů ^ƚĞĞů ĞƐŝŐŶ // ůͲEĂŚƌĂŝŶ hŶŝǀĞƌƐŝƚLJ ƌ͘ >ĂŝƚŚ K^KEK>d :K/Ed^͗ ϭϭ ^ƚƌƵĐƚƵƌĂů ^ƚĞĞů ĞƐŝŐŶ // ůͲEĂŚƌĂŝŶ hŶŝǀĞƌƐŝƚLJ ƌ͘ >ĂŝƚŚ K^KEK>d :K/Ed^͗ ϭϮ Structural Steel Design II College of Engineering Civil Engineering Department Lecture five- Welded Connections 5.1 Introduction: Welding is a process by which metallic parts are connected by heating their surfaces to a plastic or fluid state and allowing the parts to flow together and join (with or without the addition of other molten metal). The adoption of structural welding was quite slow for several decades, because many engineers thought that welding had two major disadvantages: (1) Welds had reduced fatigue strength, compared with riveted and bolted connections, and (2) it was impossible to ensure a high quality of welding without unreasonably extensive and costly inspection. 1 Structural Steel Design II College of Engineering Civil Engineering Department Lecture five- Welded Connections 5.1 Introduction: The American Welding Society’s Structural Welding Code is the generally recognized standard for welding in the United States. AWS develops codes, recommended practices, and guides under strict ANSI procedures. The AISC Specification clearly states that the provisions of the AWS Codeapply under the AISC Specification, with only a few minor exceptions, and these are listed in AISC Specification J2. 2 Structural Steel Design II College of Engineering Civil Engineering Department Lecture five- Welded Connections The first advantage is economic, because the use of welding permits large savings in pounds of steel used. Welded structures allow the elimination of a large percentage of the gusset and splice plates necessary for bolted structures, as well as the elimination of bolt heads. In some bridge trusses, it may be possible to save up to 15 percent or more of the steel weight. Welding has a much wider range of application than bolting. Consider a steel pipe column and the difficulties of connecting it to other steel members by bolting. A bolted connection may be virtually impossible, but a welded connection presents few difficulties. Welded structures are more rigid, because the members often are welded directly to each other. Frequently, the connections for bolted structures are made through intermediate connection angles or plates that deform due to load transfer, making the entire structure more flexible. 3 Structural Steel Design II College of Engineering Civil Engineering Department Lecture five- Welded Connections 5.2 ADVANTAGES OF WELDING: The process of fusing pieces together creates the most truly continuous structures. Fusing results in one-piece construction, and because welded joints are as strong as or stronger than the base metal, no restrictions have to be placed on the joints. It is easier to make changes in design and to correct errors during erection (and less expensive) if welding is used. Another item that is often important is the relative silence of welding. Fewer pieces are used, and as a result, time is saved in detailing, fabrication, and field erection. 4 Structural Steel Design II College of Engineering Civil Engineering Department Lecture five- Welded Connections 5.3 WELDING METHODS There are essentially four main types of welding procedures used in structural applications: 1) Shielded Metal Arc Welding (SMAW) 2) Gas Metal Arc Welding (GMAW) 3) Flux Cored Arc Welding (FCAW) 4) Submerged Arc Welding (SAW) 5 Structural Steel Design II College of Engineering Civil Engineering Department Lecture five- Welded Connections 5.3 WELDING METHODS: 1. Shielded Metal Arc Welding (SMAW) is also known as manual, stick, or hand welding. An electric arc is produced between the end of a coated metal electrode and the steel components to be welded. 6 Structural Steel Design II College of Engineering Civil Engineering Department Lecture five- Welded Connections 2. Gas Metal Arc Welding (GMAW) is also known as MIG welding. It is fast and economical. A continuous wire is fed into the welding gun. This process may be automated. 7 Structural Steel Design II College of Engineering Civil Engineering Department Lecture five- Welded Connections 3. Flux Cored Arc Welding (FCAW) is similar to GMAW, but the filler wire has a center core that contains flux. 8 Structural Steel Design II College of Engineering Civil Engineering Department Lecture five- Welded Connections 4. Submerged Arc Welding (SAW) is only performed by automatic or semiautomatic methods. Uses a continuously fed filler metal electrode. The Weld pool is protected from the surrounding atmosphere by a blanket of granular flux fed at the welding gun. Results in a deeper weld penetration than the other process. Only flat or horizontal positions may be used. 9 Structural Steel Design II College of Engineering Civil Engineering Department Lecture five- Welded Connections 5.4 CLASSIFICATION OF WELDS: Three separate classifications of welds are described in this section. These classifications are based on the types of welds made, the positions of the welds, and the types of joints used. 5.4.1 Type of Weld: The two main types of welds are the fillet welds and the groove welds. In addition, there are plug and slot welds, which are not as common in structural work. These four types of welds are shown in Fig. 5.1. Fillet weld: are those made where parts lap over each other, as shown in Fig. 5.1(a). They may also be used in tee joints. Fillet welds are the most economical welds to use, as little preparation of the parts to be connected is necessary. In addition, these welds can be made very well by welders of somewhat lesser skills than those required for good work with other types of welds. 10 Structural Steel Design II College of Engineering Civil Engineering Department Welded Connections The fillet welds will be shown to be weaker than groove welds, although most structural connections (about 80 percent) are made with fillet welds. Groove weld: as illustrated in Fig. 5.1(b) and (c) (which are welds made in grooves between the members to be joined) are used when the members to be connected are lined up in the same plane. Nevertheless, groove welds are quite common for many connections, such as column splices, butting of beam flanges to columns, etc., and they make up about15 percent of structural welding. Groove welds can be either complete-penetration welds, which extend for the full thickness of the part being connected, or partial penetration welds, which extend for only part of the member thickness. 12 Structural Steel Design II College of Engineering Civil Engineering Department Welded Connections 5.4.1 Type of Weld: Fillet welds Groove welds FIGURE 5.1 Types of structural welds. 13 Structural Steel Design II College of Engineering Civil Engineering Department Welded Connections Groove welds are generally more expensive than fillet welds because of the costs of preparation. In fact, groove welds can cost up to 50 to 100 percent more than fillet welds. Plug and slot weld: plug weld is a circular weld that passes through one member into another, thus joining the two together. The slot may be partly or fully filled with weld material. These welds are shown in Fig. 5.1(d). These two expensive types of welds may occasionally be used when members lap over each other and the desired length of fillet welds cannot be obtained. They may also be used to stitch together parts of a member, such as the fastening of cover plates to a built-up member. 14 Structural Steel Design II Al-Nahrain University Dr. Laith Khalid Kamil Chapter 14 College of Engineering Dr. Ahmed Abdalhafedh Mustafa Civil Engineering Department Chapter14- Welded Connections 5.4.2 Weld Position: Welds are referred to as flat, horizontal, vertical, or overhead—listed in order of their economy, with the flat welds being the most economical and the overhead welds being the most expensive. A moderately skilled welder can do a very satisfactory job with a flat weld, but it takes the very best to do a good job with an overhead weld. Although the flat welds often are done with an automatic machine, most structural welding is doneby hand. We indicated previously that the assistance of gravity is not necessary for theforming of good welds, but it does speed up the process. The globules of the molten electrodes can be forced into the overhead welds against gravity, and good welds will result; however, they are slow and expensiveto make, so it is desirable to avoid them whenever possible. These types of welds are shown in Fig. 5.2. 16 15 Structural Steel Design II College of Engineering Civil Engineering Department Welded Connections FIGURE 5.2 Weld positions. 5.4.3 Type of Joint: Welds can be further classified according to the type of jointused: butt, lap, tee, edge, corner, etc. See Fig. 5.3. FIGURE 5.3: Types of weld joints. 17 Structural Steel Design II College of Engineering Civil Engineering Department Welded Connections 5.4 FILLET WELDS: Tests have shown that fillet welds are stronger in tension and compression than they are in shear, so the controlling fillet weld stresses given by the various specifications are shearing stresses. When practical, it is desirable to try to arrange welded connections so that they will be subjected to shearing stresses only, and not to a combination of shear and tension or shear and compression. When fillet welds are tested to failure with loads parallel to the weld axes, they seem to fail by shear at angles of about 45˚ through the throat. Their strength is therefore assumed to equal the design shearing stress or allowable shear stress times the theoretical throat area of the weld. The theoretical throats of several fillet welds are shown in Fig. 5.4. The throat area equals the theoretical throat distance times the length of the weld. 1 8 Structural Steel Design II College of Engineering Civil Engineering Department Welded Connections FIGURE 5.4: (a) Convex surface. (b) Concave surface. (c) Unequal leg fillet weld. 2 Structural Steel Design II College of Engineering Civil Engineering Department Welded Connections In this figure, the root of the weld is the point at which the faces of the original metal pieces intersect, and the theoretical throat of the weld is the shortest distance from the root of the weld to its diagrammatic face. For the 45˚ or equal leg fillet, the throat dimension is 0.707 times the leg of the weld, but it has a different value for fillet welds with unequal legs. The desirable fillet weld has a flat or slightly convex surface, although the convexity of the weld does not add to its calculated strength. At first glance, the concave surface would appear to give the ideal fillet weld shape, because stresses could apparently flow smoothly and evenly around the corner,with little stress concentration. Years of experience, however, have shown that single-pass fillet welds of a concave shape have a greater tendency to crack upon cooling, and this factor has proved to be of greater importance than the smoother stress distribution of convex types. 3 Structural Steel Design II College of Engineering Civil Engineering Department Welded Connections Another item of importance pertaining to the shape of fillet welds is the angle of the weld with respect to the pieces being welded. The desirable value of this angle is in the vicinity of 45˚. For 45˚ fillet welds, the leg sizes are equal, and such welds are referred to by the leg sizes (e.g., a 1/4-in fillet weld). Should the leg sizes be different (not a 45˚ weld), both leg sizes are given in describing the weld (e.g., a 3/8- by-1/2-in fillet weld). 4 Structural Steel Design II College of Engineering Civil Engineering Department Welded Connections 5.5 Welding Symbols: Weld symbols are used to communicate the specific detailsand requirements of each weld to the welder. Weld symbols are included on fabrication and erection drawings. It is certainly desirable for steel designers and draftsmen to use this standardized system. The Table shown presents the various welding symbols developed by the American Welding Society. 5 Structural Steel Design II College of Engineering Civil Engineering Department Welded Connections 5 Structural Steel Design II College of Engineering Civil Engineering Department Welded Connections 5.6 Strength of Welds: The stress in a fillet weld is usually said to equal the load divided by the effective throat area of the weld, with no consideration given to the direction of the load. Tests have shown, however, that transversely loaded fillet welds are appreciably stronger than ones loaded parallel to the weld’s axis. Transverse fillet welds are stronger for two reasons: First, they are more uniformly stressed over their entire lengths, while longitudinal fillet welds are stressed unevenly, due to varying deformations along their lengths; second, tests show that failure occurs at angles other than 45˚, giving them larger effective throat areas. The method of determining the strength of fillet welds along their longitudinal axes, regardless of the load directions, is usually used to simplify computations. It is rather common for designers to determine the strength of all fillet welds by assuming that the loads are applied in the longitudinal direction. 6 Structural Steel Design II College of Engineering Civil Engineering Department Welded Connections 5.6 Strength of Welds: It is rather common for designers to determine the strength of all fillet welds by assuming that the loads are applied in the longitudinal direction. FIGURE 5.5: (a) Longitudinal fillet weld. (b) Transverse fillet weld. (c) Transverse and longitudinal welds. 7 Structural Steel Design II College of Engineering Civil Engineering Department Welded Connections 5.7 AISC Requirements: When welds are made, the electrode material should have properties of the base metal. If the properties are comparable, the weld metal is referred to as the matching base metal. (That is, their nominal strengths are similar.) Table 14.1 (which is Table J2.5 of the AISC Specification) provides nominal strengths for various types of welds, including fillet welds, plug and slot welds, and complete-penetration and partial-penetration groove welds. The design strength of a particular weld (ФRn) and the allowable strength (Rn /Ω) of welded joints shall be the lower value of the base material strengthdetermined according to the limit states of tensile rupture and shear rupture, and the weld metal strength determined according to the limit state of rupture by the expressions to follow: 7 Structural Steel Design II College of Engineering Civil Engineering Department Welded Connections For the base metal, the nominal strength is: Rn = FnBM ABM (AISC Equation J2-2) For the weld metal, the nominal strength is Rn = Fnw Awe (AISC Equation J2-3) In the preceding equations: FnBM =nominal stress of the base metal, ksi Fnw =nominal stress of the weld metal, ksi ABM =area of the base metal, in2 Awe =area of the weld, in2 8 Structural Steel Design II College of Engineering Civil Engineering Department Welded Connections AISC Specification (Table J2.5) Available Strength of Welded Joints 9 Structural Steel Design II College of Engineering Civil Engineering Department Welded Connections Table J2.5 in AISC Specification provides the weld values needed touse these equations: Ф, Ω, FBM and Fw. Limitations on these values are also given in this table. The filler metal electrodes for shielded arc welding are listed as E60XX, E70XX, etc. In this classification, the letter E represents an electrode, while the first set of digits (60, 70, 80, 90, 100, or 110) indicates the minimum tensile strength of the weld, in ksi. The remaining digits may be used to specify the type of coating. Because strength is the most important factor to the structural designer, we usually specify electrodes as E70XX, E80XX, or simply E70, E80, and so on. For the usual situation, E70 electrodes are used for steels with Fy values from 36 to 60 ksi, while E80 is used when Fy is 65 ksi. 10 Structural Steel Design II College of Engineering Civil Engineering Department Welded Connections There are several other provisions applying to welding given in Section J2.2b of the LRFD Specification. Among the more important are the following: 1. The minimum length of a fillet weld may not be less than four times the nominal leg size of the weld. Should its length actually be less than this value, the weld size considered effective must be reduced to one-quarter of the weld length. 2. The maximum size of a fillet weld along edges of material less than 1/4 in thick equals the material thickness. For thicker material, it may not be larger than the material thickness less 1/16 in, unless the weld is specially built out to give a full throat thickness. For a plate with a thickness of 1/4 in or more, it is desirable to keep the weld back at least 1/16 in from the edge so that the inspector can clearly see the edge of the plate and thus accurately determine the dimensions of the weld throat. 11 Structural Steel Design II College of Engineering Civil Engineering Department Welded Connections 3. The minimum permissible size fillet welds of the AISC Specification are given in Table 14.2 (Table J2.4 of the AISC Specification).They vary from 1/8 in for 1/4 in or thinner material up to 5/16 in for material over 3/4 in in thickness. AISC Specification (Table J2.4) 12 Structural Steel Design II College of Engineering Civil Engineering Department Welded Connections 4. When longitudinal fillet welds are used for the connection of plates or bars, their length may not be less than the perpendicular distance between them, because of shear lag (discussed in Chapter 3). 5. For lap joints, the minimum amount of lap permitted is equal to five times the thickness of the thinner part joined, but may not be less than 1 in (AISC J2.2b). The purpose of this minimum lap is to keep the joint from rotating excessively. 6. Should the actual length (l) of an end-loaded fillet weld be greater than 100 times its leg size (w), the AISC Specification (J2.2b) states that, due to stressvariations along the weld, it is necessary to determine a smaller or effective length for strength determination. This is done by multiplying l by the term (β), as given in the following equationin which w is the weld leg size: 13 Structural Steel Design II College of Engineering Civil Engineering Department Welded Connections β = 1.2 – 0.002 (L/w) ≤ 1.0 (AISC Equation J2-1) If the actual weld length is greater than 300 w, the effective length shall be taken to be equal to 0.6. 5.8 Design Of Simple Fillet Welds: Examples 5-1 and 5-2 demonstrate the calculations used to determine the strength of various fillet welded connections; Example 5-3 presents the design of such a connection. 14 Structural Steel Design II College of Engineering Civil Engineering Department Welded Connections Example 5-1 (A) Determine the design strength of a 1-in length of a 1/4-in fillet weld formed by the shielded metal arc process (SMAW) and E70 electrodes with a minimum tensile strength FEXX = 70 ksi. Assume that load is to be applied parallel to the weld length. (B) Repeat part (a) if the weld is 20 in long. (C) Repeat part (a) if the weld is 30 in long. 15 Structural Steel Design II College of Engineering Civil Engineering Department Welded Connections Example 5-1 16 Structural Steel Design II College of Engineering Civil Engineering Department Welded Connections Example 5-2 What is the design strength of the connection shown in Figure, if the plates consist of A572 Grade 50 steel E70 electrodes were used, and the 7/16-in fillet welds were made by the SMAW process. 17 Structural Steel Design II College of Engineering Civil Engineering Department Welded Connections 18 Structural Steel Design II College of Engineering Civil Engineering Department Welded Connections 19 Structural Steel Design II College of Engineering Civil Engineering Department Welded Connections Example 5-3 Using 50 ksi steel and E70 electrodes, design SMAW fillet welds to resist a full- capacity load on the 3/8 X 6-in member shown in Figure. 20 Structural Steel Design II College of Engineering Civil Engineering Department Welded Connections Example 5-3 : Solution: 21 Structural Steel Design II College of Engineering Civil Engineering Department Welded Connections Example 5-3 : Solution: 22 Structural Steel Design II College of Engineering Civil Engineering Department Welded Connections 5.9 Design of Connections for Members with Both Longitudinal and Transverse Fillet Welds: 23 Structural Steel Design II College of Engineering Civil Engineering Department Welded Connections 5.8 Design of Connections for Members with Both Longitudinaland Transverse Fillet Welds: Example 5-4: Determine the total LRFD design strength of the 5/16-in E70 fillet welds shown in the Figure. 24 Structural Steel Design II College of Engineering Civil Engineering Department Welded Connections 25
