# The Lrfd Code Provisions Accounting Essay

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Steel design, or more specifically, structural steel design, is an area of knowledge of structural engineering used to design steel structures. The structures can range from schools to homes to bridges. There are currently two schools of thought in steel design. The oldest is the permissible stress design Allowable Strength Design (ASD) method. The second, and most recent, is the Load and Resistance Factor Design (LRFD) method.

## 3.16 Allowable Strength Design (ASD)

In allowable stress design (ASD), the Designer must size the anchorage such that the service load does not exceed the allowable load for any anchor:

Tservice â‰¤ Tallowable

Vservice â‰¤ Vallowable

The Designer must read the allowable load from the applicable table and adjust the allowable load for all applicable design parameters for the anchor, such as spacing, edge distance, in-service temperature or allowable stress increase for short-term loads

## 3.17 LRFD

Design according to the provisions for LRFD satisfies the requirements of the AISC Specification when the allowable strength of each structural component equals or exceeds the required strength determined on the basis of the LRFD load combinations. LRFD is a method of proportioning structures such that no applicable limit state is exceeded when the structure is subjected to all appropriate design load combinations.

The first difference between ASD and LRFD, historically, has been that the old Allowable Stress Design compared actual and allowable stresses while LRFD compares required strength to actual strengths. ASD is the simple method & LRFD is the sophisticated one. ASD combines dead and live loads and treats them in the same way. In LRFD different load factors are assigned to dead loads and live loads, which is appealing while changes is load factors and resistance factors are much easier to make in LRFD.

For LRFD, the required strength, Ru, is determined from the following factored load combinations:

1.4D

1.2D + 1.6L + 0.5(Lr or S or R)

1.2D + 1.6(Lr or S or R) + (0.5L or 0.8W)

1.2D + 1.6W + 0.5L + 0.5(Lr or S or R)

1.2D ± 1.0E + 0.5L + 0.2S

0.9D ± (1.6W or 1.0E)

## 3.18 ADVANTAGES

## 1.Safety in the design is obtained by specifying that the reduced nominal strength of a designed structure is less than the effect of factored loads acting on the structure.

2 LRFD accounts for both variability in load and resistance. It achieves fairly uniform levels of safety for different limit states

## 3.19 DESIGN OF MEMBERS FOR TENSION

3.20 SLENDERNESS LIMITATIONS

As per Load Resistance Factored Design (LRFD) code section D1 there is no maximum slenderness limit for the design of member in tension but slenderness ratio preferably should not exceed 300.This limitation does not apply to rods or hangers in tension.

3.21.TENSILE STRENGTH

As per Load Resistance Factored Design (LRFD) code section D2 ,The design tensile strength Ï†t , Pn ,and the allowable tensile strength of tension members shall be the minimum of the tensile yielding in the gross section or the tensile rupture in the net section.

3.21.1 FOR TENSILE YIELDING IN THE GROSS SECTION

Pn = Fy Ag (Equation 3.48)

According to LRFD code provisions Eq D2-1

Ï†t= 0.90

where

Fy = specified minimum yield stress of the type of steel being used in Ksi(MPa)

Ag = gross area of member in2 (mm2)

3.21.2 FOR TENSILE RUPTURE IN THE NET SECTION

Pn = Fu Ae (Equation 3.49)

According to LRFD code provisions Eq D2-2

Ï†t= 0.75

where

Fu = specified minimum tensile strength of the type of steel being used in ksi (MPa)

Ae = effective net area, in2 (mm2)

3.23 AREA DETERMINATION

As per Load Resistance Factored Design (LRFD) code section D3, Gross area Ag of a member is the total cross sectional area and net area An of member is the sum of the product thickness and the net width of each element computed as follows:

3.23.1 FOR BOLT

The width of a bolt hole should be taken as 1.6 in greater than the nominal dimension of the hole.

3.23.2 FOR A CHAIN OF HOLES

The net width of the hole shall be obtained by deducting from the gross width , the sum of the diameter or slot dimensions of all the holes.For each gage space in the chain ,the quantity is :

(Equation 3.50)

where

s= longitudinal center to center spacing of any two consecutives holes in in.(mm)

g= transverse center to center spacing between fastener gage lines in in.(mm)

3.23.3.EFFECTIVE NET AREA

The effective area of tension member shall be determined as follows

Ae = An U (Equation 3.51)

According to LRFD code provisions Eq D3-1

Where

U= the shear lag factor and it is determined as shown in table

Table 3.4.1 SHEAR LAG FACTORS FOR TENSION MEMBERS

CASE

DESCRIPTION OF ELEMENT

SHEAR LAG FACTOR,U

1

All tension members where the tension load is transmitted directly to each member of the cross section by means of fasteners or welds

U=1.0

2

All tension members , except plates and HSS , where the tension load is transmitted to some of the cross section elements by fastener and longitudinal welds

U = 1- X/l

3

All tension members where the tension load is transmitted by transverse welds to some but not all of the cross section elements

U = 1.0

and

An = area of the directly connected elements

As per Load Resistance Factored Design (LRFD) code table D3.1

3.24 PIN CONNECTED MEMBERS

As per Load Resistance Factored Design (LRFD) code section D5

3.24.1 TENSILE STRENGTH

See section 2.1

3.24.2 FOR TENSILE RUPTURE IN THE NET EFFECTIVE AREA

Pn = 2tbeff Fu (Eq. 3.52)

According to LRFD code provisions Eq D5-1

Ï†t =0.75

where,

t = thickness of plate , in (mm)

beff = 2t+ 0.63 in but not more than the actual distance from the edge of the whole to

the edge of the part measured in the direction normal to the applied force

3.24.3 FOR TENSILE RUPTURE IN THE EFFECTIVE AREA

Pn = 0.6Fu Asf (Equation 3.53)

According to LRFD code provisions Eq D5-2

Î¦sf = 0.75

Where

Asf = 2t(a + ) , in2 (mm2 ) (Equation 3.54)

3.25 DESIGN OF MEMBERS FOR COMPRESSION

3.26 GENERAL PROVISIONS

As per Load Resistance Factored Design (LRFD) code section E1, The design compressive strength Ï†c Pn , and the allowable compressive strength are determined as follows :

According to the limits of flexure buckling, the nominal compressive strength shall be the lowest value obtained.

1. For singly and doubly symmetric members the limit state of flexure buckling is applicable.

2.For singly symmetric and unsymmetrical members and certain doubly symmetric members such as built up columns the limit states of flexure buckling is also applicable

Ï†c = 0.9

3.27 SLENDERNESS LIMITATIONS AND EFFECTIVE LENGTH

As per Load Resistance Factored Design (LRFD) code section E2, For members designed on the basis of compression the slenderness ratio should not exceed 200

Where

L = laterally unbraced length of the member , in. (mm)

r = governing radius of gyration , in. (mm)

K= the effective length factor

3.28 COMPRESSIVE STRENGTH FOR FLEXURE BUCKLING OF MEMBERS

WITHOUT SLENDER ELEMENTS

As per Load Resistance Factored Design (LRFD) code section E3 ,When the torsional unbraced length is larger then the lateral unbraced length this section may be designed as wide flange and similarly shaped columns.

The nominal compressive strength Pn shall be determined based on the limit state of flexure buckling

Pn = Fcr Ag (Equation 3.55)

According to LRFD code provisions Eq E3-1

The flexure buckling stress Fcr is determined as follows :

when

(Equation 3.56)

According to LRFD code provisions Eq E3-2

when

Fe < .44 Fy

Fcr = 0.877 Fe (Equation 3.57)

According to LRFD code provisions Eq E3-3

Where

Fe = elastic critical buckling stress

Fe = (Equation 3.58)

According to LRFD code provisions Eq E3-4

3.29 SINGLE ANGLE COMRESSION MEMBER

As per Load Resistance Factored Design (LRFD) code section E5, When the members are evaluated as axially loaded compression members ,the effects of eccentricity on single angles members to be neglected when using one of the effective slenderness ratios.

1.Members are loaded at the ends in compression through the same one leg.

2.Members are attached by welding or my minimum two bolt connections.

3.There are no intermediate transverse loads

3.29.1 For equal leg angles on unequal leg angles connected through the longer leg that

are individual members or are web members of planar trusses with adjacent web

members attached to the same side of gusset plate or chord

1.when 0 80

= 72+0.75 (Equation 3.59)

According to LRFD code provisions Eq E5-1

2. When > 80

= 32 + 1.25 200 (Equation 3.60)

According to LRFD code provisions Eq E5-2

For unequal leg angles with leg length ratios less than 1.7 and connected through the shorter leg shall be increased by adding 4 [( bl / bs )2 -1], but of the member shall not be less then 0.95

3.29.2 For equal leg angles on unequal leg angles connected through the longer leg that

are individual members of box or spaced trusses with adjacent web members

attached to the same side of gusset plate or chord

1. when 0

= 60 + 0.8 (Equation 3.61)

According to LRFD code provisions Eq E5-3

2. When > 75

= 45 + 200 (Equation 3.62)

According to LRFD code provisions Eq E5-4

For unequal leg angles with leg length ratios less than 1.7 and connected through the shorter leg shall be increased by adding 6 -1], but of the member shall not be less then 0.82

Where

L= length of member between work points at truss chord centerlines in. (mm)

bl = longer leg of angle in. (mm)

bs = shorter leg of angle in. (mm)

rx radius of gyration of geometric axis parallel to connected leg, in (mm)

rz = radius of gyration for the minor principal axis in (mm)

3.29.3 Single angle member with different end conditions with leg length ratios greater

then 1.7 or with transverse loading shall be evaluated for combined axial load and

flexure using the provisions.

3.30 BUILT UP MEMBERS

As per Load Resistance Factored Design (LRFD) code section E6.

3.30.1 COMPRESSIVE STRENGTH

The nominal compressive strength composed of two or more shapes that are interconnected by bolts or welds can be determined in accordance with Section 2.3 , 2 .If the buckling mode involves relative deformation that produces shear forces in the connector between individual shapes ( )m determined as follows :

1. For intermediate connector that are bolted:

( )m = (Equation 3.63)

According to LRFD code provisions Eq E6-1

For intermediate connector that are welded:

( )m = (Equation 3.64)

According to LRFD code provisions Eq E6-2

( )m = modified column slenderness of built up member.

( )o = column slenderness of built up member acting as a unit in the buckling

direction being considered.

a = distance between connectors in (mm)

ri = minimum radius of gyration of individual component in. (mm)

rib = radius of gyration of individual component related to its centroidal axis

parallel to member axis of buckling in. (mm)

Î± = separation ratio

h = distance between centroids of individual component perpendicular of member

axis of buckling in. (mm)

3.30.2 DIMENSIONAL REQUIEMENTS.

Individual components of compression members composed of two or more shapes shall be connected to one another at intervals a such that the effective slenderness ratio of each of the component shapes, between the fasteners does not exceed three-fourth times the governing slenderness ratio of the built-up member. The lead radius of gyration ri shall be used in computing the slenderness ratio of each component parts.

3.31 MEMBERS WITH SLENDER ELEMENTS

As per Load Resistance Factored Design (LRFD) code section E7 ,It applies to compression members with slender section for uniformly compressed elements , their nominal compressive strength Pn shall be determined based on the limit state of flexure buckling

Pn = Fcr Ag (Equation 3.65)

According to LRFD code provisions Eq E7-1

When

(Equation 3.66)

According to LRFD code provisions Eq E7-2

When

(Equation 3.67)

According to LRFD code provisions Eq E7-3

Q = 1 for members with compact and non-compact sections

= Qs , Qa for members with slender element section For cross sections composed of only unstiffed slender elements, Q = .for cross sections of only stiffed slender elements, Q= . For cross sections composed of both stiffened and unstiffened slender elements, Q=

3.31.1 SLENDER UNSTIFF ELEMENT Qs

The reduction factor Qs for slender unstiff elements is defined as :

3.31.1.1 for flanges, angles and plates projecting from rolled column or other

compression members:

1.When

Qs = 1 (Equation 3.68)

According to LRFD code provisions Eq E7-4

2.When

Qs = 1.415 -0.74 () (Equation 3.69)

According to LRFD code provisions Eq E7-5

3.When

Qs = (Equation 3.70)

According to LRFD code provisions Eq E7-6

3.31.1.2 For flanges, angles and plates projecting from built up columns or other

compression members:

1.When

Qs = 1

According to LRFD code provisions Eq E7-7

2.When 1.17

Qs = 1.415 -0.65 (Equation 3.71)

According to LRFD code provisions Eq E7-8

3.When >1.17

Qs = (Equation 3.72)

According to LRFD code provisions Eq E7-9

Where,

and shall not be taken less than 0.35 nor greater than 0.76 for calculation purposes.

3.31.1.3 for single angles

1. when

Qs = 1

According to LRFD code provisions Eq E7-10

2. When 0.45

Qs = 1.34 -0.76 (Equation 3.73)

According to LRFD code provisions Eq E7-11

3.when

Qs = (Equation 3.74)

According to LRFD code provisions Eq E7-12

b= full width of longest angle leg in. (mm)

for stems of Tees

1.When

Qs = 1

According to LRFD code provisions Eq E7-13

2.When

Qs = 1.908 - 1.22 (Equation 3.75)

According to LRFD code provisions Eq E7-14

3.When

Qs = (Equation 3.76)

According to LRFD code provisions Eq E7-15

b= width of unstiff compression element in.( mm )

d= full nominal depth of tee in. (mm)

t= thickness of element, in. (mm)

3.31.2 SLENDER STIFFENED ELEMENT Qs

The reduction factor Qa for slender stiffened element is defined as follows :

Qa = (Equation 3.77)

According to LRFD code provisions Eq E7-16

Where

A = total cross section area of member in2 (mm2)

Aeff = summation of the effective areas of the cross section based on the reduce effective

width be in2 (mm2)

The reduced effective width can be determined as follows

3.31.2.1.for uniformly compressed slender elements with except flanges

of square rectangular section of uniform thickness

t (Equation 3.78)

According to LRFD code provisions Eq E7-17

where f is taken as Fcr with Fcr calculated based on Q=1

3.31.2.2.For flanges of square and rectangular slender element section of uniform

thickness with

t (Equation 3.79)

According to LRFD code provisions Eq E7-18

Where f =

3.31.2.3 For axially loaded circular sections

0.11 <

Q = Qa = (Equation 3.80)

According to LRFD code provisions Eq E7-19

Where

D = outside diameter in. (mm)

t= wall thickness in. (mm)