STRC06_SteelPart2_0715

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Steel (Part 2)

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Lesson Overview

Chapter 4: Structural Steel Design (Part 2) • Plastic Design • Design of Tension Members • Design of Bolted Connections • Design of Welded Connections • Plate Girders • Composite Beams

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Learning Objectives

You will learn how to • use statical and mechanism design methods for plastic design • design bolted and welded connections for a range of loading conditions • account for tension field action in plate girders

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Prerequisite Knowledge

You should already be familiar with • load combinations • design for flexure • design for shear • design for compression

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Referenced Codes and Standards

• International Building Code (IBC, 2012) • Minimum Design Loads for Buildings and Other Structures (ASCE/SEI7, 2010) • Seismic Design Manual (AISC, 2012) • Specification for Structural Steel Buildings (AISC 360, 2010) • Steel Construction Manual (AISC, 2011)

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Plastic Method of Structural Analysis

This method • is used to determine the maximum loads a structure can support prior to collapse • is applicable to structures constructed with a ductile material possessing ideal elastic plastic characteristics • calculates the point that extreme fibers reach yield stress: M_y = F_yS • shows whole section yielded as M = F Z nomenclature S elastic section modulus Z plastic section modulus (arithmetic sum of the first moments of area about the neutral axis)

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Plastic Method of Structural Analysis

Figure 4.16 Plastic Moment of Resistance Figure 4.15 Elastic‐Plastic Material

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Statical Design Method

procedure • Apply factored loads to the statically determinate cut‐back structure. • Fig. 4.18(a) • Draw free bending moment diagram. • Fig. 4.18(b) • Superimpose fixing moment line. • Fig. 4.18(c) • Make moments at supports 2 and 3 and in spans 12 and 34 equal to M_p. • Solve for M_pfrom geometry.

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Statical Design Method

Figure 4.18 Statical Design Method

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Mechanism Design Method

• Apply a virtual displacement to each potential plastic hinge mechanism and equate internal and external work. • solve for M_pusing equations (see next slide) for • beam mechanism • sway mechanism • combined mechanism • The largest value of M_p governs. Figure 4.19 Mechanism Design Method

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Example: Mechanism Design Method

Example 4.29

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Example: Mechanism Design Method

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Example: Mechanism Design Method

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Column Design Requirements

• Flanges and webs of members subjected to combined flexure and compression must be compact (AISC 360 Table B4.1). • Webs of W sections must also comply with AISC 360 Eq. A‐1‐1 and Eq. A‐1‐2. • In accordance with AISC 360 App. 1.2.4, the axial load in a column with plastic hinges may not exceed 0.75ϕ_cA_gF_y.

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Example: Column Design Requirements

Example 4.31

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Example: Column Design Requirements

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Example: Column Design Requirements

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Design of Tension Members

section overview • plates in tension • rolled section in tension • design for fatigue

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Plates in Tension

For yielding of gross section, AISC 360 Sec. D2 gives • design strength • allowable strength For tensile rupture, AISC 360 Sec. D2 gives • design strength • allowable strength

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Plates in Tension

Figure 4.20 Effective Net Area of Bolted Connection

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Effective Net Area–Bolted Connections

• effective net area, A_e, of a bolted connection • (Section numbers refer to bolted plates in Fig. 4.20.) • effective hole diameter for standard size holes

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Effective Net Area–Welded Connections

AISC 360 Sec. D3.1 gives the effective net area as follows. • flat plate with longitudinal welded connection • flat plate with transverse fillet welded connection (shown in Fig. 4.21) • shear lag factor, U Figure 4.21 Welded Connections for Plates

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Example: Plates in Tension

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Example: Plates in Tension

Example 4.32

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Example: Plates in Tension

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Rolled Sections in Tension–Bolted Connections

• effective net area • shear lag factor • 0.60 ≤ U ≤ 0.90 l distance between first and last fasteners in line ̅ distance from connection plane member centroid nomenclature

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AISC 360 Eq. D3‐1

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Rolled Sections in Tension–Bolted Connections

AISC 360 Table D3.1 permits the adoption of the following values for the shear lag factor. • U = 0.90 for T, W, M, and S shapes with b_f ≥ 2d/3, connected by the flange, with not fewer than three bolts in line in the direction of stress. • U = 0.85 for T, W, M, and S shapes with b_f < 2d/3, connected by the flange, with not fewer than three bolts in line in the direction of stress. • U= 0.70 for T, W, M, and S shapes connected by the web, with not less than four bolts in line in the direction of stress. • U= 0.80 for single or double angles with not less than four bolts in line in the direction of stress. • U= 0.60 for single or double angles with two or three bolts in line in the direction of stress.

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Rolled Sections in Tension–Welded Connections

• force transmitted only by transverse welds • force transmitted by longitudinal welds nomenclature l distance between first and last fasteners in line ̅ distance from connection plane member centroid

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AISC Eq. D3‐1

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Rolled Sections in Tension–Welded Connections

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Example: Rolled Sections in Tension

Example 4.33

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Example: Rolled Sections in Tension

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Example: Rolled Sections in Tension

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Poll: Design for Fatigue

Is the following statement true or false? Fatigue effects in design account for the age of steel members and connections. (A) true (B) false

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Poll: Design for Fatigue

Is the following statement true or false? Fatigue effects in design account for the age of steel members and connections. (A) true (B) false Solution Fatigue is the weakening of a material caused by repeatedly applied loads. Fatigue effects are not necessarily related to age. The answer is (B) false.

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© 2015 Professional Publications, Inc. 41 STRC ©2015 Professional Publications, Inc. • Fatigue failure is caused by fluctuations of tensile stress that cause crack propagation. • Establish applicable loading condition from AISC 360 Table A‐3.1. • stress categories A, B, B´, C, D, E, and E´ • stress category F • F_THis the maximum stress range for indefinite design life (i.e., infinite number of cycles).

Design for Fatigue

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Design for Fatigue

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Example: Design for Fatigue

Example 4.34

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Example: Design for Fatigue

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Example: Design for Fatigue

AISC 360 Table A‐3.1 Fatigue Design Parameters (partial table shown)

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Reproduced from Steel Construction Manual, Fourteenth ed., 2012. American Institute of Steel Construction, Inc., Chicago, IL. The range of the load is 57 kips.

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Design of Bolted Connections

section overview • types of bolts • bearing‐type bolts in shear and tension • slip‐critical bolts in shear and tension • bolts in bearing • bolt group eccentrically loaded in plane of the faying surface • bolt group eccentrically loaded normal to the faying surface

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Types of Bolts

common bolts • grade A307 with a nominal tensile strength of 45 kips/in2 • used in bearing‐type or snug‐tight connections only high‐strength bolts • grade A325, F182, A354 BC, and A449 with a nominal tensile strength of 90 kips/in2 • grade A490, F2280, and A354 BD with a nominal tensile strength of 113 kips/in2 • used in bearing‐type, pretensioned and slip‐critical connections

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Types of Bolt Connections

bearing‐type (snug‐tight) • must be tightened sufficiently to bring plies into firm contact • transfer of load depends on bearing of bolts against side of holes • no specific level of installed tension specified • may be used when pretensioned or slip‐critical connections not required pretensioned • Bolts must be pretensioned to a minimum of 70% of bolt’s tensile strength. • faying surfaces may be uncoated, coated, or galvanized without regard to the slip coefficient obtained • transfer of load depends on bearing of bolts against side of holes

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Types of Bolt Connections

slip‐critical • required to be pretensioned to a minimum of 70% of bolt’s tensile strength • load transferred through friction • at strength limit state, connection slips, so bolts may be in bearing

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Types of Bolt Connections

Pretensioned connections are required when bearing‐type connections are used in • column splices in buildings over 125 ft tall • bracing members in buildings over 125 ft tall (see AISC 360 Sec. J1.10) • structures carrying cranes of over 5 ton capacity • supports of machinery causing impact or stress reversal Slip‐critical connections are required where • fatigue load occurs • bolts are used in oversize holes or slotted holes parallel to the direction of load • slip at the faying surfaces will affect the performance of the structure • bolts are used in conjunction with welds

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Bearing‐Type Bolts in Shear and Tension

F_nv nominal shear strength of bolt R_n nominal shear capacity Φ resistance factor Ω safety factor nomenclature

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Bearing‐Type Bolts in Shear and Tension

Per AISC 360 Sec. J3.3, • minimum permissible distance between centers of holes, s_min = 2.67d • preferred distance between centers of holes, s_pref = 3.0d • available strength in shear • available strength in tension (AISC 360 Sec. J3.6) AISC 360 Eq. J3‐1

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Example: Bearing‐Type Bolts in Shear and Tension

The connection shown consists of 11 grade A307 ¾ in diameter bolts. Determine the design shear strength of the bolts in the connection.

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Example: Bearing‐Type Bolts in Shear and Tension

The connection shown consists of 11 grade A307 ¾ in diameter bolts. Determine the design shear strength of the bolts in the connection. Solution From AISC Manual Table 7‐1, the available strength of the 11 bolts in shear is

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kips 8.97 11 bolts bolt 98.7 kips LRFD n nv b R F A   _{ } _   

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kips 5.97 11 bolts bolt 65.7 kips ASD n nv b R F A n    _{ } _   _ _ 

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Slip‐Critical Bolts in Shear

• minimum pretension force, T_b, in a bolt (AISC 360 Table J3.1) 0.70F_u • nominal slip resistance (AISC 360 Eq. J3‐4) • slip coefficient for class A surfaces μ = 0.35 • slip coefficient for class B surfaces μ = 0.50 • ratio of mean installed bolt tension to specified minimum bolt pretension D_u= 1.13

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Slip‐Critical Bolts in Tension

D_u bolt tension multiplier N_b number of bolts carrying the applied tension T_a applied tensile force on the bolt (ASD) T_b specified pretension force on the bolt T_u applied tensile force on the bolt (LRFD) nomenclature

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Slip‐Critical Bolts in Tension

• nominal tensile strength • available tensile strength • See AISC 360 Table J3.2 for values of nominal tensile stress, F_nt. • See AISC 360 Table 7‐2 for values of ϕR_n and R_n/Ω. • combined shear and tension • available strength in tension unaffected • available resistance to shear reduced by

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Example: Slip‐Critical Bolts in Shear and Tension

The connection shown consists of 11 grade A490 ¾ in diameter slip‐critical bolts. The bolts are in standard holes with a class A faying surface. No fillers are used. Determine the available resistance to shear of the bolts in the connection.

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Example: Slip‐Critical Bolts in Shear and Tension

The connection shown consists of 11 grade A490 ¾ in diameter slip‐critical bolts. The bolts are in standard holes with a class A faying surface. No fillers are used. Determine the available resistance to shear of the bolts in the connection. Solution For bolts in standard holes and with a class A faying surface, AISC Manual Table 7‐3 gives the available single shear strength of the 11 bolts in shear as

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11.9 kips 11 bolts 131 kips LRFD n R   

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7.91 kips 11 bolts 87 kips ASD n R   

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Bolts in Bearing

d_b nominal bolt diameter D_n nominal hole diameter F_u tensile strength of the critical connected part L_c clear distance, in the direction of force, between edge of hole and edge of adjacent hole or edge of the connected part L_e edge distance, in the direction of force, between the bolt center and the edge of the connected part R_n nominal bearing capacity S bolt center‐to‐center spacing t thickness of the connected part nomenclature symbols Φ resistance factor Ω safety factor

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Bolts in Bearing

• Bearing strength must be checked for both bearing‐type bolts and slip‐critical bolts. • nominal bearing strength (AISC 360 Eq. J3‐6a and Eq. J3‐6b) • when deformation is a design consideration, • when deformation is not a design consideration, • available bearing strength • See AISC Manual Tables 7‐5 and 7‐6 for values of ϕR_n and R_n/Ω.

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Example: Bolts in Bearing

The connection shown consists of 11 grade A307 ¾ in diameter bolts in

standard holes. Plate thickness is 0.5 in.

The edge distance is L_c = 2.5 in, s = 3 in,

and F_u = 58 ksi. Determine the available

bearing strength of the bolts in the A36 plates.

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Example: Bolts in Bearing

The connection shown consists of 11 grade A307 ¾ in diameter bolts in standard holes. Plate thickness is 0.5 in.

The edge distance is L_c = 2.5 in, s = 3 in,

and F_u = 58 ksi. Determine the available bearing strength of the bolts in the A36 plates. Solution From AISC Manual Table 7‐5, the minimum edge distance for full bearing strength is L_c = 2.25 in < 2.5 in [provided] The edge distance does not govern.

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Example: Bolts in Bearing

From AISC Manual Table 7‐4, the available strength of the 11 bolts in bearing is

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kips in 62.0 0.5 in 11 bolts bolt 341 kips LRFD n R             

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kips in 41.3 0.5 in 11 bolts bolt 227 kips ASD n R             

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Poll: Eccentrically Loaded Connections

Is the following statement true or false? A bolt group loaded eccentrically has a higher capacity than one loaded through its centroid. (A) true (B) false

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Poll: Eccentrically Loaded Connections

Is the following statement true or false? A bolt group loaded eccentrically has a higher capacity than one loaded through its centroid. (A) true (B) false Solution The higher the eccentricity of the applied load, the lower the design strength of a bolt group. Moments, along with shear, are applied to the bolt group. The answer is (B) false.

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Bolt Group Eccentrically Loaded in Plane of Faying Surface

• vertical force on bolt i due to applied load, P_r • vertical force on bolt i due to eccentricity, e • horizontal force on bolt i due to eccentricity • horizontal force on bolt i due to eccentricity, e • resultant force on bolt i due to eccentricity, e

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Bolt Group Eccentrically Loaded in Plane of Faying Surface

Figure 4.23 Eccentrically Loaded Bolt Group

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Example: Bolt Group Eccentrically Loaded in Plane of Faying Surface

Example 4.38

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Example: Bolt Group Eccentrically Loaded in Plane of Faying Surface

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Example: Bolt Group Eccentrically Loaded in Plane of Faying Surface

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Example: Bolt Group Eccentrically Loaded in Plane of Faying Surface

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Bolt Group Eccentrically Loaded Normal to Faying Surface (LRFD)

• tensile force in each bolt above the neutral axis due to the eccentricity • shear force in each bolt due to the applied load d_m moment arm between resultant tensile and compressive forces in the bolts e Eccentricity n number of bolts in the connection n' number of bolts above the neutral axis P_u Required axial strength nomenclature

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Bolt Group Eccentrically Loaded Normal to Faying Surface (LRFD)

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Example: Bolt Group Eccentrically Loaded Normal to Faying Surface (LRFD)

Example 4.39

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Assume that threads are not excluded from the shear plane.

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Example: Bolt Group Eccentrically Loaded Normal to Faying Surface (LRFD)

Example 4.39

Assume that threads are not excluded from the shear plane.

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Example: Bolt Group Eccentrically Loaded Normal to Faying Surface (LRFD)

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Bolt Group Eccentrically Loaded Normal to Faying Surface (ASD)

• tensile force in a bolt a distance, y_i, from neutral axis • shear force in each bolt due to applied load

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Bolt Group Eccentrically Loaded Normal to Faying Surface (ASD)

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Example: Bolt Group Eccentrically Loaded Normal to Faying Surface (ASD)

Example 4.40

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Example: Bolt Group Eccentrically Loaded Normal to Faying Surface (ASD)

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Example: Bolt Group Eccentrically Loaded Normal to Faying Surface (ASD)

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Design of Welded Connections

section overview • Weld Design Strength • Complete‐Penetration Groove Weld • Partial‐Penetration Groove Weld • Fillet Weld Design Considerations • Weld Group Eccentrically Loaded in Plane of Faying Surface • Weld Group Eccentrically Loaded Normal to Faying Surface

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Weld Design Strength

• strength of welded connection depends on both base metal and weld metal strength • Weld nominal stress values, effective areas, resistance factors, and safety factors are tabulated in AISC 360 Table J2.5. • nominal strength of weld metal (AISC 360 Eq. J2‐3) R_n = F_nwA_we • nominal strength of base metal (AISC 360 Eq. J2‐2) R_n = F_nBMA_BM

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Complete‐Penetration Groove Weld

• nominal strength governed by base metal • computation of strength of weld not required • thinner part joined is the effective thickness, t_e Figure 4.26 Complete‐Penetration Groove Weld

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Example: Complete‐Penetration Groove Weld

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Example: Complete‐Penetration Groove Weld

Example 4.41

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Partial‐Penetration Groove Weld

Nominal strength is governed by effective throat thickness, t_e Figure 4.27 Partial‐Penetration Groove Weld

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Example: Partial‐Penetration Groove Weld

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Example: Partial‐Penetration Groove Weld

Example 4.42

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Example: Partial‐Penetration Groove Weld

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Fillet Weld

• Leg length, w, is used to designate nominal weld size. • effective throat thickness (AISC 360 Sec. J2.2a) t_e = 0.707w • Minimum permissible length of fillet weld is four times the nominal weld size. Figure 4.28 Fillet Weld

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Fillet Weld

• Permitted minimum (AISC 360 Table J2.4) and maximum weld sizes (AISC 360 Sec. J2.2b) are shown in Table 4.2 and Table 4.3. • When longitudinal fillet welds are used alone in a connection, the length of each fillet weld must not be less than the perpendicular distance between them, because of shear lag. Table 4.2 Minimum Size of Fillet Welds Table 4.3 Maximum Size of Fillet Welds

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Fillet Weld

Nominal strength of a linear weld group is R_n = F_wA_w where F_w= 0.60F_EXX(1.0 + 0.50sin1.5θ) Nominal strength of a concentrically loaded weld group is the greater of R_n = R_wl + R_wt or R_n = 0.85R_wl + 1.5R_wt

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Fillet Weld

A_BM effective area of base metal A_w effective area of weld metal F_BM nominal strength of base metal F_EXX weld metal classification strength F_w nominal strength of weld metal R_wl total nominal strength of longitudinally loaded fillet welds R_wt total nominal strength of transversely loaded fillet welds θ angle of inclination of loading measured from weld longitudinal axis nomenclature symbols

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Available Strength of a 1/16 in Fillet Weld

To simplify calculations, determine available strength of a ⁄ in fillet weld per inch run of E70XX grade electrodes. • LRFD method, design strength • ASD method, allowable strength

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Example: Counting in Sixteenths

Example 4.43

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Example: Counting in Sixteenths

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Example: Counting in Sixteenths

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Fillet Weld Size Governed by Base Metal Thickness

• capacity of weakest shear plane governs design of welded connection • design shear strength of weld per linear inch • design shear rupture strength per linear inch, with grade 50 base material (AISC 360 Eq. J4‐4) • largest effective weld size

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Fillet Weld Size Governed by Base Metal Thickness

Table 4.4 Effective Weld Size

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Example: Effective Fillet Weld Size

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Example: Effective Fillet Weld Size

Example 4.44

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Strength of Fillet Weld Groups

methods presented in AISC 360 Sec. J2.4 • AISC 360 Sec. J2.4(a): linear weld group with uniform leg size loaded through center of gravity • AISC 360 Sec. J2.4(b): instantaneous center of rotation method • AISC 360 Sec. J2.4(c): weld group with concentric loading with uniform leg size and elements oriented longitudinally or transversely to direction of applied load

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Example: Weld Design Strength

Example 4.45

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Example: Weld Design Strength

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Example: Weld Design Strength

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Example: Weld Design Strength

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Weld Group Eccentrically Loaded in Plane of Faying Surface

• polar moment of inertia of weld group about centroid • vertical force per linear inch of weld due to P_r • vertical force at i due to e • horizontal force at i due to e • resultant force at i

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Weld Group Eccentrically Loaded in Plane of Faying Surface

Figure 4.29 Eccentrically Loaded Weld Group l total length of weld P_r applied load i point i e eccentricity nomenclature

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Example: Weld Group Eccentrically Loaded in Plane of Faying Surface

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Example: Weld Group Eccentrically Loaded in Plane of Faying Surface

Example 4.46

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Example: Weld Group Eccentrically Loaded in Plane of Faying Surface

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Example: Weld Group Eccentrically Loaded in Plane of Faying Surface

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© 2015 Professional Publications, Inc. 125 STRC ©2015 Professional Publications, Inc. • vertical force per linear inch of weld due to p_r • moment of inertia about x‐axis • horizontal force at i due to e • resulting force at i

Weld Group Eccentrically Loaded Normal to Faying Surface

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Weld Group Eccentrically Loaded Normal to Faying Surface

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Example: Weld Group Eccentrically Loaded Normal to Faying Surface

Example 4.47

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Example: Weld Group Eccentrically Loaded Normal to Faying Surface

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Example: Weld Group Eccentrically Loaded Normal to Faying Surface

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Example: Weld Group Eccentrically Loaded Normal to Faying Surface

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Plate Girders

section overview • girder proportions • design for flexure • design for shear without tension field action • design for shear with tension field action • design of intermediate stiffeners • design of bearing stiffeners

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Girder Proportions

typical overall girder depth L/12 < d < L/10 typical flange width h/5 < b_f < h/3 intermediate stiffeners not required when unstiffened web requires

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Figure 4.31 Plate Web Girder

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Girder Proportions

requirements for web with stiffeners • For a/h > 1.5, • For a/h ≤ 1.5, Refer to AISC 360 Sec. F5, F13, G2, and G3. Figure 4.31 Plate Web Girder AISC Eq. F13‐4 AISC Eq. F13‐3

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Example: Girder Proportions

Example 4.48

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Example: Girder Proportions

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Design for Flexure

• web slender if • Nominal flexural strength, M_n, is less than plastic moment, M_p. • Flexural is design of girder governed by AISC 360 Sec. F5. • flexural strength of girder governed by the following limit states • compression flange yielding • lateral‐torsional buckling • compression flange local buckling

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AISC Eq. F5‐1 AISC Eq. F5‐2 AISC Eq. F5‐7

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Example: Design for Flexure

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Example: Design for Flexure

Example 4.49

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Example: Design for Flexure

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Example: Design for Flexure

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Poll: Tension Field Action

Is the following statement true or false? Tension field action is the post‐buckling development of diagonal tensile stresses in slender plate‐girder web panels and compressive forces in the transverse stiffeners that border those panels. (A) true (B) false

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Poll: Tension Field Action

Is the following statement true or false? Tension field action is the post‐buckling development of diagonal tensile stresses in slender plate‐girder web panels and compressive forces in the transverse stiffeners that border those panels. (A) true (B) false The answer is (A) true.

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Tension Field Action

• induced when elastic critical load, enhanced by stiffeners, is reached • Stiffeners in compression and girder web in tension produce an equivalent Pratt truss. • design using tension field action not permitted in • end‐panels • panels with large hole • large panel aspect ratios Figure 4.32 Tension Field Action

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© 2015 Professional Publications, Inc. 147 STRC ©2015 Professional Publications, Inc. • For , V_n is governed by shear yielding of web. C_v = 1.0 (AISC 360 Eq. G2‐3) • For , where C_v = right portion of equation for this case (AISC 360 Eq. G2‐4), V_n is governed by inelastic buckling of web. • For , V_n is governed by elastic buckling of web • AISC Manual Tables 3‐16a and 3‐17a provide values of φ_vV_n/A_wand V_n/Ω_bA_w for a range of values of h/t_wand a/h.

Design for Shear Without Tension Field Action

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Example: Design for Shear Without Tension Field Action

Example 4.50

Reproduced from Steel Construction Manual, Fourteenth ed., 2012. American Institute of Steel Construction, Inc., Chicago, IL.

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Example: Design for Shear Without Tension Field Action

Example 4.50

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Example: Design for Shear Without Tension Field Action

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Design for Shear With Tension Field Action

• V_n determined in accordance with AISC 360 Sec. G3.2

• AISC Manual Tables 3‐16b and 3‐17b provide values of φ_vV_n/A_wand V_n/Ω_bA_wfor a

range of values of h/t_wand a/h.

• tension field action not permitted in end panels and when a/h > 3.0 or

a/h > (260t_w/h)2

(Along with other cases per AISC 360 Sec. G3.1, nominal shear strength is given by AISC 360 Sec. G2.1 as .)

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Example: Design for Shear With Tension Field Action

Example 4.51

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Example: Design for Shear With Tension Field Action

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Example: Design for Shear With Tension Field Action

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Design of Intermediate Stiffeners

tension field action excluded • From AISC 360 Sec. G2.2, required moment of inertia of stiffener is • maximum allowable width‐to‐ thickness ratio of a stiffener = 0.56 See AISC 360 Eq. G3‐3. tension field action included • the minimum transverse stiffener moment of inertia is • fabrication detail: stiffener stopped short of tension flange to avoid fatigue cracking (does not apply to bearing stiffeners) AISC Eq. G2‐7

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1 1 2 1 2 1 r c st st st st c c V V I I I I V V       _ _    AISC Eq. G3‐4

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Example: Design of Intermediate Stiffeners

Example 4.52

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Example: Design of Intermediate Stiffeners

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Example: Design of Intermediate Stiffeners

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Design of Bearing Stiffeners

• required when applied load exceeds web’s yielding, crippling, or sidesway buckling capacity • designed as axially loaded cruciform column, including • 25t_wweb strip (interior) • 12t_wweb strip (ends) • effective length factor, K = 0.75 (AISC 360 Sec. J10.8) • nominal bearing strength, R = 1.8F A AISC 360 Eq. J7‐1 • available bearing strength Figure 4.33 Bearing Stiffeners

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Example: Design of Bearing Stiffeners

Example 4.53

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Example: Design of Bearing Stiffeners

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Example: Design of Bearing Stiffeners

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Composite Beams

section overview • section properties • shear connection • deck ribs parallel to steel beam • deck ribs perpendicular to steel beam • design for flexure

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Section Properties

• if sufficient shear connector ensures full composite action, depth of stress block is

• if insufficient shear connectors are provided, depth of stress block is

• From AISC Manual Table 3‐20, lower bound on the actual moment of inertia, I_LB_, is

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Section Properties

For the composite beam shown in Fig. 4.35, the effective width of the concrete slab, on either side of the beam centerline, is the lesser of • ⁄ of the beam span • ⁄ of the beam spacing • the distance to the edge of the slab Figure 4.35 Fully Composite Beam Section Properties

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Example: Section Properties

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Example: Section Properties

Example 4.54

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Example: Section Properties

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Shear Connection

A_sc cross‐sectional area of a stud F_u tensile strength of a stud E_c modulus of elasticity of concrete w unit weight of concrete R_g stud group coefficient R_p stud position coefficient nomenclature

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Shear Connection

• Shear force transferred across interface is the lesser of • Provide n = V'/Q_n connectors on either side of maximum moment. • AISC 360 Eq. I8‐1 gives nominal strength of one stud shear connector as

• R_g and R_p parameters are provided in

AISC 360 Sec. I8‐2a.

• Shear connector placement limitations

are provided in AISC 360 Sec. I8‐2a and Fig. 4.34.

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Shear Connection

Figure 4.36 Placement of Shear Connectors

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Deck Ribs Parallel to Steel Beam

• Maximum permitted diameter of stud shear connectors is 2.5 times the thickness of the base metal. • Maximum connector spacing is 18 in. • R_g = 1.0 [when w_r≥ 1.5h_r] • R_g= 0.85 [when w_r < 1.5h_r] • R_p = 0.75

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Deck Ribs Parallel to Steel Beam

Figure 4.37 Deck Ribs Parallel to Steel Beam, R_gand R_pValues

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Deck Ribs Perpendicular to Steel Beam

stud group coefficient • R_g= 1.0 [one stud welded in steel deck rib] • R_g= 0.85 [two studs welded in steel deck rib] • R_g= 0.70 [three or more studs welded in steel deck rib] stud position coefficient • R_p = 0.75 [studs welded in steel deck

rib with e_mid-ht ≥ 2 in]

• R_p = 0.60 [studs welded in steel deck

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Deck Ribs Perpendicular to Steel Beam

Figure 4.38 Deck Ribs Perpendicular to Steel Beams, R_gValues

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Deck Ribs Perpendicular to Steel Beam

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Example: Shear Connection

Example 4.55

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Example: Shear Connection

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Example: Shear Connection

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Design for Flexure

• φM_nfor range of Y₁, Y₂, and ΣQ_nis

found in AISC Manual Table 3‐19. • From AISC 360 Sec. I3.2d, ΣQ_n is the least of • 0.85 • F_yA_s • nQ_n • Design to support total factored loads for shored and unshored construction. • Steel beam alone must support all loads before concrete attains 75% of its strength.

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Example: Design for Flexure

Example 4.56 Example 4.54

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Example: Design for Flexure

Example 4.56

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Learning Objectives

You have learned how to • use statical and mechanism design methods for plastic design • design bolted and welded connections for a range of loading conditions • account for tension field action in plate girders

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Lesson Overview

Chapter 4: Structural Steel Design, Part 2 • Plastic Design • Design of Tension Members • Design of Bolted Connections • Design of Welded Connections • Plate Girders • Composite Beams