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68402/61420Slide # : Structural Design of Buildings II Design of Connections Monther Dwaikat Assistant Professor Department of Building Engineering An-Najah National University

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68402/61420Slide # 2 Types of Connections Simple Bolted Shear Connections Simple Welded Connections Bolted Connections

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68402/61420Slide # 3 Types of Connections Simple Connections Bolted Connections Welded Connections Common Bolts High Strength Bolts Slip Critical Bearing Type Filet Weld Groove Weld Eccentric Connections

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68402/61420Slide # 4 Types of Connections Simple Connections Bolted Connections Welded Connections Elastic Analysis Eccentric Connections Ultimate Analysis Moment Resisting Elastic Analysis Ultimate Analysis Moment Resisting

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68402/61420Slide # 5 Simple Bolted Connections There are different types of bolted connections. They can be categorized based on the type of loading. Tension member connection and splice. It subjects the bolts to forces that tend to shear the shank. Beam end simple connection. It subjects the bolts to forces that tend to shear the shank. Hanger connection. The hanger connection puts the bolts in tension

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68402/61420Slide # 6 Simple Bolted Connections Tension member Connection/ splice Beam end Simple shear connection P P P P

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68402/61420Slide # 7 Simple Bolted Connections PP P Hanger connection (Tension) Moment resisting connection

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68402/61420Slide # 8 Simple Bolted Connections The bolts are subjected to shear or tension loading. In most bolted connection, the bolts are subjected to shear. Bolts can fail in shear or in tension. You can calculate the shear strength or the tensile strength of a bolt Simple connection: If the line of action of the force acting on the connection passes through the center of gravity of the connection, then each bolt can be assumed to resist an equal share of the load. The strength of the simple connection will be equal to the sum of the strengths of the individual bolts in the connection.

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68402/61420Slide # 9 Bolt Types & Materials A307 - Unfinished (Ordinary or Common) bolts low carbon steel A36, F u = 413 MPa, for light structures under static load A325 - High strength bolts, heat-treated medium carbon steel, F u = 827 MPa, for structural joints A490 - High strength bolts, Quenched and Tempered Alloy steel, F u = 1033 MPa for structural joints A449 - High strength bolts with diameter > 1 ½”, anchor bolts, lifting hooks, tie-downs

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68402/61420Slide # 10 Common Bolts ASTM A307 bolts Common bolts are no longer common for current structural design but are still available

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68402/61420Slide # 11 High Strength Bolts High strength bolts (HSB) are available as ASTM A 325 and ASTM A490 Slip Critical Bearing Type Courtesy of Kao Wang Screw Co., Ltd. Advantages of HSB over A307 bolts Fewer bolts will be used compared to 307 cheaper connection! Smaller workman force required compared to 307 Higher fatigue strength Ease of bolt removal changing connection

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68402/61420Slide # 12 High Strength Bolts Snug tight All plies of the connection are in firm contact to each other: No pretension is used. Easer to install and to inspect Pre-tensioned Bolts are first brought to snug tight status Bolts are then tensioned to 70% of their tensile stresses Courtesy of Bolts are tensioned using direct tension indicator, calibrated wrench or other methods (see AISC) Slip critical Bolts are pre-tensioned but surfaces shall be treated to develop specific friction. The main difference is in design, not installation. Load must be limited not to exceed friction capacity of the connection (Strength Vs. Serviceability!) Necessary when no slip is needed to prevent failure due to fatigue in bridges.

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68402/61420Slide # 13 HSB – Bearing Type Connections The shear strength of bolts shall be determined as follows A A325 Type X ThreadType N ThreadType If the level of threads is not known, it is conservative to assume that the threads are type N. AISC Table J3.2 The table bellow shows the values of f v (MPa) for different types of bolts

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68402/61420Slide # 14 Bolted Shear Connections We want to design the bolted shear connections so that the factored design strength ( R n ) is greater than or equal to the factored load. R n P u So, we need to examine the various possible failure modes and calculate the corresponding design strengths. Possible failure modes are: Shear failure of the bolts Failure of member being connected due to fracture or yielding or …. Edge tearing or fracture of the connected plate Tearing or fracture of the connected plate between two bolt holes Excessive bearing deformation at the bolt hole

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68402/61420Slide # 15 Failure Modes of Bolted Connections Bolt Shearing Tension Fracture Plate Bearing Block Shear

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68402/61420Slide # 16 Actions on Bolt Shear, bearing, bending P P P P P P P/2 P P Lap Joint Butt Joint Bearing and single plane Shear Bending Bearing and double plane Shear

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68402/61420Slide # 17 Bolted Shear Connections Possible failure modes Failure of bolts: single or double shear Failure of connected elements: Shear, tension or bending failure of the connected elements (e.g. block shear) Bearing failure at bolt location Single shear Double shear

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68402/61420Slide # 18 Bolted Shear Connections Shear failure of bolts Average shearing stress in the bolt = f v = P/A = P/( d b 2 /4) P is the load acting on an individual bolt A is the area of the bolt and db is its diameter Strength of the bolt = P = f v x ( d b 2 /4)where f v = shear yield stress = 0.6F y Bolts can be in single shear or double shear as shown above. When the bolt is in double shear, two cross-sections are effective in resisting the load. The bolt in double shear will have the twice the shear strength of a bolt in single shear.

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68402/61420Slide # 19 Bolted Shear Connections

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68402/61420Slide # 20 Bolted Shear Connections Failure of connected member We have covered this in detail in this course on tension members Member can fail due to tension fracture or yielding. Bearing failure of connected/connecting part due to bearing from bolt holes Hole is slightly larger than the fastener and the fastener is loosely placed in hole Contact between the fastener and the connected part over approximately half the circumference of the fastener As such the stress will be highest at the radial contact point (A). However, the average stress can be calculated as the applied force divided by the projected area of contact

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68402/61420Slide # 21 Bolted Shear Connections Average bearing stress f p = P/(d b t), where P is the force applied to the fastener. The bearing stress state can be complicated by the presence of nearby bolt or edge. The bolt spacing and edge distance will have an effect on the bearing strength. Bearing stress effects are independent of the bolt type because the bearing stress acts on the connected plate not the bolt. A possible failure mode resulting from excessive bearing close to the edge of the connected element is shear tear-out as shown below. This type of shear tear-out can also occur between two holes in the direction of the bearing load. R n = 2 x 0.6 F u L c t = 1.2 F u L c t

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68402/61420Slide # 22 The bearing strength is independent of the bolt material as it is failure in the connected metal The other possible common failure is shear end failure known as “shear tear-out” at the connection end Bolted Shear Connections Shear limitationBearing limitation

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68402/61420Slide # 23 Bolted Shear Connections

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68402/61420Slide # 24 Bolted Shear Connections

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68402/61420Slide # 25 Spacing and Edge-distance requirements The AISC code gives guidance for edge distance and spacing to avoid tear out shear NOTE: The actual hole diameter is 1.6 mm bigger than the bolt, we use another 1.6 mm for tolerance when we calculate net area. Here use 1.6 mm only not 3.2 Bolt spacing is a function of the bolt diameter Common we assume The AISC minimum spacing is AISC Table J3.4

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68402/61420Slide # 26 Bolt Spacings & Edge Distances Bolt Spacings - Painted members or members not subject to corrosion: 2 2/3d ≤ Bolt Spacings ≤ 24t or 305 mm (LRFD J3.3) (LRFD J3.5) - Unpainted members subject to corrosion: 3d ≤ Bolt Spacings ≤ 14t or 178 mm Edge Distance Values in Table J3.4M ≤ Edge Distance ≤ 12t or 152 mm (LRFD J3.4) (LRFD J3.5) d - bolt diameter t - thickness of thinner plate

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68402/61420Slide # 27 Bolted Shear Connections To prevent excessive deformation of the hole, an upper limit is placed on the bearing load. This upper limit is proportional to the fracture stress times the projected bearing area R n = C x F u x bearing area = C F u d b t If deformation is not a concern then C = 3, If deformation is a concern then C = 2.4 C = 2.4 corresponds to a deformation of 6.3 mm. Finally, the equation for the bearing strength of a single bolts is R n where, = 0.75 and R n = 1.2 L c t F u < 2.4 d b t F u L c is the clear distance in the load direction, from the edge of the bolt hole to the edge of the adjacent hole or to the edge of the material

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68402/61420Slide # 28 Bolted Shear Connections This relationship can be simplified as follows: The upper limit will become effective when 1.2 L c t F u > 2.4 d b t F u i.e., the upper limit will become effective when L c > 2 d b If L c < 2 d b,R n = 1.2 L c t F u If L c > 2 d b,R n = 2.4 d b t F u F u - specified tensile strength of the connected material L c - clear distance, in the direction of the force, between the edge of the hole and the edge of the adjacent hole or edge of the material. t - thickness of connected material

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68402/61420Slide # 29 Important Notes L c – Clear distance

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68402/61420Slide # 30 Design Provisions for Bolted Shear Connections In a simple connection, all bolts share the load equally.

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68402/61420Slide # 31 Design Provisions for Bolted Shear Connections In a bolted shear connection, the bolts are subjected to shear and the connecting/connected plates are subjected to bearing stresses.

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68402/61420Slide # 32 Design Provisions for Bolted Shear Connections The shear strength of all bolts = shear strength of one bolt x number of bolts The bearing strength of the connecting / connected plates can be calculated using equations given by AISC specifications. The tension strength of the connecting / connected plates can be calculated as discussed in tension members.

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68402/61420Slide # 33 AISC Design Provisions Chapter J of the AISC Specifications focuses on connections. Section J3 focuses on bolts and threaded parts AISC Specification J3.3 indicates that the minimum distance (s) between the centers of bolt holes is A distance of 3d b is preferred. AISC Specification J3.4 indicates that the minimum edge distance (L e ) from the center of the bolt to the edge of the connected part is given in Table J3.4. Table J3.4 specifies minimum edge distances for sheared edges, edges of rolled shapes, and gas cut edges.

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68402/61420Slide # 34 AISC Design Provisions AISC Specification indicates that the maximum edge distance for bolt holes is 12 times the thickness of the connected part (but not more than 152 mm). The maximum spacing for bolt holes is 24 times the thickness of the thinner part (but not more than 305 mm). Specification J3.6 indicates that the design tension or shear strength of bolts is F n A b = 0.75 Table J3.2, gives the values of F n A b is the unthreaded area of bolt. In Table J3.2, there are different types of bolts A325 and A490.

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68402/61420Slide # 35 AISC Design Provisions The shear strength of the bolts depends on whether threads are included or excluded from the shear planes. If threads are included in the shear planes then the strength is lower. We will always assume that threads are included in the shear plane, therefore less strength to be conservative. We will look at specifications J3.7 – J3.9 later. AISC Specification J3.10 indicates the bearing strength of plates at bolt holes. The design bearing strength at bolt holes is R n R n = 1.2 L c t F u ≤ 2.4 d b t F u - deformation at the bolt holes is a design consideration

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68402/61420Slide # 36 Common bolt terminologies A325-SC – slip-critical A325 bolts A325-N –snug-tight or bearing A325 bolts with thread included in the shear planes. A325-X -snug-tight or bearing A325 bolts with thread excluded in the shear planes. Gage – center-to-center distance of bolts in direction perpendicular to member’s axis Pitch –...parallel to member’s axis Edge Distance – Distance from center of bolt to adjacent edge of a member p g p p p Edge distance

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68402/61420Slide # 37 Ex Design Strength Calculate and check the design strength of the simple connection shown below. Is the connection adequate for carrying the factored load of 300 kN. 63 k 10 mm 120x15 mm 20 mm A325-N bolts 30 mm 60 mm 30 mm 60 mm 30 mm 300 kN

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68402/61420Slide # 38 Step I. Shear strength of bolts The design shear strength of one bolt in shear = F n A b = 0.75 x 330 x x 20 2 /4000 = 77.8 kN F n A b = 77.8 kN per bolt(See Table J3.2) Shear strength of connection = 4 x 77.8 = kN Ex Design Strength

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68402/61420Slide # 39 Step II. Minimum edge distance and spacing requirements See Table J3.4M, minimum edge distance = 26 mm for rolled edges of plates The given edge distances (30 mm) > 26 mm. Therefore, minimum edge distance requirements are satisfied. Minimum spacing = 2.67 d b = 2.67 x 20 = 53.4 mm. (AISC Specifications J3.3) Preferred spacing = 3.0 d b = 3.0 x 20 = 60 mm. The given spacing (60 mm) = 60 mm. Therefore, spacing requirements are satisfied. Ex Design Strength

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68402/61420Slide # 40 Ex Design Strength Step III. Bearing strength at bolt holes. Bearing strength at bolt holes in connected part (120x15 mm plate) At edges, L c = 30 – hole diameter/2 = 30 – ( )/2 = 19.2 R n = 0.75 x (1.2 L c t F u ) = 0.75 x (1.2 x19.2 x15x400)/1000 = kN But, R n ≤ 0.75 (2.4 d b t F u ) = 0.75 x (2.4 x 20x15x400)/1000 = 216 kN Therefore, R n = kN at edge holes. At other holes, s = 60 mm, L c = 60 – ( ) = 38.4 mm. R n = 0.75 x (1.2 L c t F u ) = 0.75x(1.2 x 38.4 x15 x400)/1000 = kN But, R n ≤ 0.75 (2.4 d b t F u ) = 216 kN. Therefore R n = kN

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68402/61420Slide # 41 Ex Design Strength Therefore, R n = 216 kN at other holes Therefore, bearing strength at holes = 2 x x = kN Bearing strength at bolt holes in gusset plate (10 mm plate) At edges, L c = 30 – hole diameter/2 = 30 – ( )/2 = 19.2 mm. R n = 0.75 x (1.2 L c t F u ) = 0.75 x (1.2 x 19.2 x 10 x 400)/1000 = 69.1 kN But, R n ≤ 0.75 (2.4 d b t F u ) = 0.75 x (2.4 x 20 x 10 x 400)/1000 = 144 kN. Therefore, R n = 69.1 kN at edge holes.

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68402/61420Slide # 42 Ex Design Strength At other holes, s = 60 mm, L c = 60 – ( ) = 38.4 mm. R n = 0.75 x (1.2 L c t F u ) = 0.75 x (1.2 x 38.4 x 10x 400)/1000 = kN But, R n ≤ 0.75 (2.4 d b t F u ) = 144 kN Therefore, R n = kN at other holes Therefore, bearing strength at holes = 2 x x = kN Bearing strength of the connection is the smaller of the bearing strengths = kN

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68402/61420Slide # 43 Ex Design Strength Connection Strength Shear strength = Bearing strength (plate) = kN Bearing strength (gusset) = kN Connection strength ( R n ) > applied factored loads ( Q) > 300Therefore ok. Only connections is designed here Need to design tension member and gusset plate

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68402/61420Slide # 44 Simple Welded Connections Structural welding is a process by which the parts that are to be connected are heated and fused, with supplementary molten metal at the joint. A relatively small depth of material will become molten, and upon cooling, the structural steel and weld metal will act as one continuous part where they are joined. P P P P

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68402/61420Slide # 45 Introductory Concepts Welding Process – Fillet Weld

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68402/61420Slide # 46 Introductory Concepts The additional metal is deposited from a special electrode, which is part of the electric circuit that includes the connected part. In the shielded metal arc welding (SMAW) process, current arcs across a gap between the electrode and the base metal, heating the connected parts and depositing part of the electrode into the molten base metal. A special coating on the electrode vaporizes and forms a protective gaseous shield, preventing the molten weld metal from oxidizing before it solidifies. The electrode is moved across the joint, and a weld bead is deposited, its size depending on the rate of travel of the electrode.

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68402/61420Slide # 47 Introductory Concepts As the weld cools, impurities rise to the surface, forming a coating called slag that must be removed before the member is painted or another pass is made with the electrode. Shielded metal arc welding is usually done manually and is the process universally used for field welds. For shop welding, an automatic or semi automatic process is usually used. Foremost among these is the submerged arc welding (SAW), In this process, the end of the electrode and the arc are submerged in a granular flux that melts and forms a gaseous shield. There is more penetration into the base metal than with shielded metal arc welding, and higher strength results.

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68402/61420Slide # 48 Introductory Concepts Other commonly used processes for shop welding are gas shielded metal arc, flux cored arc, and electro-slag welding. Quality control of welded connections is particularly difficult, because defects below the surface, or even minor flaws at the surface, will escape visual detection. Welders must be properly certified, and for critical work, special inspection techniques such as radiography or ultrasonic testing must be used.

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68402/61420Slide # 49 Introductory Concepts The two most common types of welds are the fillet weld and the groove weld. Fillet weld examples: lap joint – fillet welds placed in the corner formed by two plates Tee joint – fillet welds placed at the intersection of two plates. Groove welds – deposited in a gap or groove between two parts to be connected e.g., butt, tee, and corner joints with beveled (prepared) edges Partial penetration groove welds can be made from one or both sides with or without edge preparation.

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68402/61420Slide # 50 Welded Connections Classification of welds According to type of weld According to weld position According to type of joint Butt, lap, tee, edge or corner According to the weld process SMAW, SAW Fillet weld Groove weld Flat, Horizontal, vertical or overhead weld

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68402/61420Slide # 51 Introductory Concepts

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68402/61420Slide # 52 Weld Limit States The only limit state of the weld metal in a connection is that of fracture Yielding is not a factor since any deformation that might take place will occur over such a short distance that it will not influence the performance of the structure

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68402/61420Slide # 53 Design of Welded Connections Fillet welds are most common and used in all structures. Weld sizes are specified in 1 mm increments A fillet weld can be loaded in any direction in shear, compression, or tension. However, it always fails in shear. The shear failure of the fillet weld occurs along a plane through the throat of the weld, as shown in the Figure below.

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68402/61420Slide # 54 Design of Welded Connections root hypotenuse L – length of the weld a – size of the weld

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68402/61420Slide # 55 Design of Welded Connections Shear stress in fillet weld of length L subjected to load P = f v = If the ultimate shear strength of the weld = f w R n = R n = i.e., factor = 0.75 f w = shear strength of the weld metal is a function of the electrode used in the SMAW process. The tensile strength of the weld electrode can be 413, 482, 551, 620, 688, 758, or 827 MPa. The corresponding electrodes are specified using the nomenclature E60XX, E70XX, E80XX, and so on. This is the standard terminology for weld electrodes.

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68402/61420Slide # 56 Design of Welded Connections The two digits "XX" denote the type of coating. The strength of the electrode should match the strength of the base metal. If yield stress ( y ) of the base metal is MPa, use E70XX electrode. If yield stress ( y ) of the base metal is MPa, use E80XX electrode. E70XX is the most popular electrode used for fillet welds made by the SMAW method. E – electrode70 – tensile strength of electrode (ksi) = 482 MPa XX – type of coating

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68402/61420Slide # 57 Fillet Weld Stronger in tension and compression than in shear Fillet weld designations: 12 mm SMAW E70XX: fillet weld with equal leg size of 12 mm, formed using Shielded Metal Arc Welding Process, with filler metal electrodes having a minimum weld tensile strength of 70 ksi. 9 mm-by-12 mm SAW E110XX: fillet weld with unequal leg sizes, formed by using Submerged Arc Metal process, with filler metal electrodes having a minimum weld tensile strength of 758 MPa. Leg Throat Convex Surface Leg Throat Concave Surface Unequal leg fillet weld

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68402/61420Slide # 58 Fillet Weld Strength Stress in fillet weld = factored load/eff. throat area Limit state of Fillet Weld is shear fracture through the throat, regardless of how it is loaded Design Strength: For equal leg fillet weld:

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68402/61420Slide # 59 Design of Welded Connections Table J2.5 in the AISC Specifications gives the weld design strength f w = 0.60 F EXX For E70XX, f w = 0.75 x 0.60 x 482 = 217 MPa Additionally, the shear strength of the base metal must also be considered: R n = 0.9 x 0.6 F y x area of base metal subjected to shear where, F y is the yield strength of the base metal.

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68402/61420Slide # 60 Design of Welded Connections Strength of weld in shear = 0.75 x x a x L w x f w In weld design problems it is advantageous to work with strength per unit length of the weld or base metal. For example

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68402/61420Slide # 61 Limitations on Weld Dimensions Minimum size (a min ) Function of the thickness of the thinnest connected plate Given in Table J2.4 in the AISC specifications Maximum size (a max ) function of the thickness of the thinnest connected plate: for plates with thickness 6 mm, a max = 6 mm. for plates with thickness 6 mm, a max = t – 2 mm. Minimum length (L w ) Length (L w ) 4 aotherwise, a eff = L w / 4 a = weld size Read J2.2 b page Intermittent fillet welds:L w-min = 4 a and 38 mm.

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68402/61420Slide # 62 Limitations on Weld Size – AISC Specifications J2.2b Page The minimum length of fillet weld may not be less than 4 x the weld leg size. If it is, the effective weld size must be reduced to ¼ of the weld length The maximum size of a fillet weld along edges of material less than 6 mm thick equals the material thickness. For material thicker than 6 mm, the maximum size may not exceed the material thickness less 2 mm. (to prevent melting of base material) The minimum weld size of fillet welds and minimum effective throat thickness for partial-penetration groove welds are given in LRFD Tables J2.4 and J2.3 based on the thickness of the base materials (to ensure fusion and minimize distortion) Minimum end return of fillet weld 2 x weld size

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68402/61420Slide # 63 Limitations on Weld Dimensions Maximum effective length - read AISC J2.2b If weld length L w < 100 a, then effective weld length (L w-eff ) = L w If L w < 300 a, then effective weld length (L w-eff ) = L w (1.2 – L w /a) If L w > 300 a, the effective weld length (L w-eff ) = 0.6 L w Weld Terminations - read AISC J2.2b Lap joint – fillet welds terminate at a distance > a from edge. Weld returns around corners must be > 2 a

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68402/61420Slide # 64 Guidelines for Fillet Weld design Two types of fillet welds can be used Shielded Metal Arc Welding (SMAW) Automatic Submerged Arc Welding (SAW) AISC – Section J2.2 Shear failure plane

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68402/61420Slide # 65 Weld Symbols (American Welding Society AWS) Fillet weld on arrow side. Weld’s leg size is 10 mm. Weld size is given to the left of the weld symbol. Weld length (200 mm) is given to the right of the symbol Fillet weld, 12 mm size and 75 mm long intermitten welds 125 on center, on the far side Field fillet welds, 6 mm in size and 200 mm long, both sides. Fillet welds on both sides, staggered intermitten 10 mm in size, 50 mm long and 150 mm on center Weld all around joint Tail used to reference certain specification or process

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68402/61420Slide # 66 Guidelines for Fillet Weld design Fillet weld design can be governed by the smaller value of Weld material strength Base Metal Strength 551E80XX 482E70XX F EXX (MPa)Electrode & AISC Table J2.5 Yield Limit State

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68402/61420Slide # 67 Guidelines for Fillet Weld design The weld strength will increase if the force is not parallel to the weld Maximum weld size & Minimum weld size AISC Table J2.4

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68402/61420Slide # 68 Capacity of Fillet Weld The weld strength is a function of the angle Strength Weld governs Base metal governs Angle ( ) w = weld size

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68402/61420Slide # 69 Ex. 6.2 – Design Strength of Welded Connection Determine the design strength of the tension member and connection system shown below. The tension member is a 100 mm x 10 mm thick rectangular bar. It is welded to a 15 mm thick gusset plate using E70XX electrode. Consider the yielding and fracture of the tension member. Consider the shear strength of the weld metal and the surrounding base metal. 125 mm 12 mm 100 mm x 10 mm t = 15 mm a = 6 mm

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68402/61420Slide # 70 Ex. 6.2 – Design Strength of Welded Connection Step I. Check for the limitations on the weld geometry t min = 10 mm (member) t max = 15 mm (gusset) Therefore, a min = 5 mm - AISC Table J2.4 a max = 10 mm – 2 mm = 8 mm- AISC J2.2b page Fillet weld size = a = 6 mm - Therefore, OK! L w-min = 4 x 6 = 24 mmand38 mm - OK. L w-min for each length of the weld = 100 mm (transverse distance between welds, see J2.2b) Given length = 125 mm, which is > L min. Therefore, OK!

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68402/61420Slide # 71 Ex. 6.2 – Design Strength of Welded Connection

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68402/61420Slide # 72 Ex. 6.2 – Design Strength of Welded Connection Length/weld size = 125/6 = Therefore, maximum effective length J2.2 b satisfied. End returns at the edge corner size - minimum = 2 a = 12 mm -Therefore, OK! Step II. Design strength of the weld Weld strength = x x a x 0.60 x F EXX x L w = 0.75 x x 6 x 0.60 x 482 x 250/1000 = 230 kN Step III. Tension strength of the member R n = 0.9 x 344 x 100 x 10/1000 = 310 kN- tension yield

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68402/61420Slide # 73 Ex. 6.2 – Design Strength of Welded Connection R n = 0.75 x A e x 448- tension fracture A e = U A A e = A g = 100 x 10 = 1000 mm Therefore, R n = 336 kN The design strength of the member-connection system = 230 kN. Weld strength governs. The end returns at the corners were not included in the calculations.

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