BASIC STRUCTURAL CONCEPTS NSCP Based ASD to LRFD Design of Steel Structures
Engr. Frederick Francis M. Sison
Introduction • The update of the National Structural Code (NSCP) of the Philippines, from 2001 to 2010 introduced some minor and major changes In structural design. • A significant change is on Chapter 5 – Steel and Metal (NSCP 2010). • The design philosophy was updated from NSCP 2001’s Allowable Stress Design (ASD) to NSCP 2010’s Load and Resistance Factor Design (LRFD) and Allowable STRENGTH Design (ASD)
LRFD Development • Early 1900s: Formation of building codes begin, formalizing design process and requirements. Principle design philosophy is based on the concept of allowable stresses (ASD) • Mid 1950s: the concrete industry pioneers the strength based design philosophy • Early 1970s: First strength based design specifications introduced by the concrete industry • 1986: AISC introduces the strength based Load and Resistance Factor Design (LRFD) specification.
LRFD Development • 1989: AISC releases what was supposed to be the last ASD specification • 2005 AISC releases a combined LRFD/ASD design specification that incorporates a method for using ASD level loads with the same specification used for LRFD. • 2010 National Structural Code of the Philippines adapts AISC 2005 LRFD/ASD design philosophies
Limit State Concepts • Limit States are conditions of potential failure. • Failure being defined as any state that makes the design to be infeasible • Limit states take the general form of: Demand ≤ Capacity • Structural limit states tend to fall into two major categories: strength and serviceability
Strength Limit State • Strength based limit states are potential modes of structural failure. • For steel members, the failure may be either yielding (permanent deformation) or rupture (actual failure). • The strength based limit state can be written in the general form: Required Strength ≤ Nominal Strength
Serviceability Limit State • Serviceability limit states are those conditions that are not strength based but still may make the structure unsuitable for its intended function. • The most common are deflection, vibration, slenderness, and clearance. • Serviceability limit states can be written in the general form: Actual Behavior ≤ Allowable Behavior • Serviceability limit states tend to be less rigid requirements than strength based limit states
LRFD vs. ASD Limit State Expressions • General form: Allowable Stress Design (ASD) fa ≤ Fa/FS Allowable Strength Design (ASD) Ra ≤ Rn/Ω Load and Resistance Factor Design (LRFD) Ru ≤ φRn
LRFD vs. ASD Limit State Expressions
LRFD vs. ASD • There are three major differences between the two specifications: 1. The comparison of actual stresses to actual strengths 2. The comparison of loads to either actual or ultimate strengths 3. A difference in effective factors of safety
Strength vs. Stress • The first difference between ASD and LRFD, is that the old ASD compared actual to allowable stresses while LRFD compared required strength to actual strengths. • The difference between looking at strength vs. stresses is normally just multiplying or dividing both sides of the limit state inequalities by a section property. • The NEW Allowable Strength Design (ASD), has now switched the old stress based terminology to a strength based terminology, virtually eliminating this difference between the philosophies.
Actual vs. Ultimate
Figure illustrates the member strength level computed by LRFD/ASD on a typical steel load vs. deformation diagram.
Actual vs. Ultimate • The combined force levels (Pa, Ma, Va) for ASD are typically kept below the yield load for the member by computing member load capacity, Rn, divided by a factor of safety, Ω, that reduces the capacity to a point below yielding. • For LRFD, the combined force levels (Pu, Mu, Vu) are kept below a computed member load capacity, Rn, times a resistance factor, φ. • Consequently, if the LRFD approach is used, then load factors must be applied to the applied loads to express them in terms that are safely comparable to the ultimate strength levels.
Fixed vs. Variable Factors of Safety • The LRFD specification accounts separately for the predictability of applied loads through the use of load factors and material and construction variability through resistance factors. • The ASD specification combines the two factors in to a single factor of safety. • By breaking the factor of safety apart into the independent load and resistance factors, a more consistent effective factor of safety is obtained and can result in safer or lighter structures.
Load Combinations • Typically, each load type is expressed in terms of their service load levels. • The individual loads are then combined using load combination equations considering the probability of simultaneously occurring loads. • LRFD looks at the strength of members wherein the applied loads are increased by a load factor so that they can be safely compared with the ultimate strengths of the members (which are generally inelastic) while maintaining the actual (service) loads in the elastic region
Load Combinations • These load factors are applied in the load combination equations and vary in magnitude according to the load type and depending on the predictability of the loads • The magnitude of the LRFD load factors reflects the predictability of the loads.
Load Combinations (LRFD) 1. 1.4(D + F) 2. 1.2(D + F + T) + 1.6(L + H) + 0.5(Lr or R) 3. 1.2D + 1.6(Lr or R) + ((0.5 or 1.0)*L or 0.8W) 4. 1.2D + 1.6W + (0.5 or 1.0)*L + 0.5(Lr or R) 5. 1.2D +1.0E + (0.5 or 1.0)*L 6. 0.9D + 1.6W +1.6H 7. 0.9D + 1.0E + 1.6H
Load Combinations (ASD) 1. D + F 2. D + H + F + L + T 3. D + H + F + (Lr or R) 4. D + H + F + 0.75[L + T + (Lr or R)] 5. D + H + F (W or E/1.4)
Load Combinations • You will notice that the large load factor found in the LRFD load combinations are absent from the ASD load combination equations. • Also, the predictability of the loads is not considered. For example both dead load and live load have the same load factor in equations where there are both likely to occur at full value simultaneously. • The probability associated with accurate load determination is not considered at all in the ASD method.
Comparing LRFD and ASD Load Combinations • LRFD and ASD loads are not directly comparable because they are used differently by the design codes. • LRFD loads are generally compared to member or component STRENGTH whereas ASD loads are compared to member or component allowable values that are less than the full strength of the member or component. • We can compare them at service levels by computing an equivalent service load from each combination.
Comparing LRFD and ASD Load Combinations • Consider a steel tension member that has a nominal axial capacity, Pn, and is subjected to a combination of dead and live loads. We will use φ = 0.90 and Ω =1.67 • Let Ps,equiv equals the algebraic sum of D and L: Ps,equiv = D + L • The controlling ASD load combination equation in this case is: Pn = 1.0*D + 1.0*L = 1.0*(D+L) = 1.0*Ps,equiv
Comparing LRFD and ASD Load Combinations • We can now determine the equivalent total load allowed by ASD by using the design inequality: Ps,equiv ≤ Pn / Ω Ps,equiv ≤ Pn / 1.67 = 0.60Pn Ps,equiv / Pn ≤ 0.60
Comparing LRFD and ASD Load Combinations • The controlling LRFD load combination equation in this case is: Pu = 1.2D + 1.6L • We make the following definitions: D = (X%)Ps,equiv and L = (1-X%)Ps.equiv • Where X is the percentage of Ps,equiv that is dead load. Substituting into the load combination: Pu = 1.2(X)Ps,equiv + 1.6(1-X)Ps,equiv = [1.6 – 0.4X]Ps,equiv
Ps,equiv = Pu / [1.6-0.4X]
Comparing LRFD and ASD Load Combinations • Substituting the above expression into the LRFD version of the design inequality, we get: Pu ≤ Pn [1.6 = 0,4X]Ps,equiv ≤ φPn Ps,equiv / Pn ≤ 0.90 / [1.6 – 0.4X]
Comparing LRFD and ASD Load Combinations
Comparing LRFD and ASD Load Combinations • For this example, whenever the total service load is 25% dead load, ASD gives greater capacity • ASD allows more actual load on the structure. Otherwise, LRFD is more advantageous. • The variable factor of safety associated with LRFD is considered to be more consistent with probability • A structure that is subjected to predominantly live loads required greater factor of safety that is provided by ASD
LRFD of Tension Members • General Form: Tu ≤ φtTn Where: Tu = LRFD factored loads Tn = nominal tensile yielding strength of the member = FyAg or FuAe φt = reduction factor for tensile yielding
• Limit States to consider: 1. Slenderness 2. Tensile yielding 3. Tensile Rupture • Slenderness Limitations (serviceability limit state) L/r should not exceed 300
Design of Tension Members • For tensile yielding in the gross section
φt = 0.90 (LRFD); Ωt = 1.67 (ASD) • For tensile rupture in the net section
φt = 0.75 (LRFD); Ωt = 2.00 (ASD) • Example: Select an 8 in. W-shape, ASTM A992, section Dead load = 30 kips Live load = 90 kips length of member = 25 ft.
Design of Tension Members
• Calculate the required tensile strength LRFD
ASD
Tu = 1.2(30 kips) + 1.6(90 kips) Tu = 180 kips
Ta = 30 kips + 90 kips) Ta = 120 kips
Design for Tension Members • Check tensile yield limit state LRFD
ASD
φtTn = (0.9)(50 ksi)(6.16 in2) 277 kips > 180 kips
Tn /Ω= (50 ksi)(6.16 in2)/1.67 184 kips > 120 kips
• Check tensile rupture strength LRFD
ASD
φtTn = (0.75)(65 ksi)(4.32 in2) 211 kips > 180 kips
Tn /Ω= (65 ksi)(4.32 in2)/2.00 141 kips > 120 kips
• Check slenderness limit L/r = (25.0 ft/1.26 in)(12.0 in/ft) = 238 < 300
Design of Compression Members • General Form: Pu ≤ φcPn Where: Pu = LRFD factored loads Pn = nominal compressive strength of the member = FcrAg ; Fcr = flexural buckling stress φc = reduction factor for compressive strength = 0.90
• Limit States to consider: 1. Slenderness 2. Flexural buckling • Slenderness Limitations (serviceability limit state) KL/r should not exceed 200
Design of Compression Members • Flexural Buckling Limitations Then:
Else:
Where: Fe = π2E/(KL/r)2 = Euler Critical Buckling Stress Q = 1 for compact and non-compact sections Q = QsQa for slender sections KL = effective length
Design for Compression Members Example: Calculate the strength of W14x90 Solution: Governing
= 58.6
Calculate elastic critcial buckling stress
Design of Compression Members Calculate flexural buckling stress: Since
;
LRFD
ASD
Design of Flexural Members • General Form:
Mu ≤ φbMn
Where: Mu = LRFD factored loads Mn = nominal flexural strength of the member φb = reduction factor for flexural strength = 0.90
• Limit States to consider: 1. Flexural yielding 2. Lateral-Torsional Buckling 3. Live Load Deflection • Live Load Deflection Criterion (serviceability limit state) maximum deflection should be less than L/360
Design of Flexural Members Nominal flexural strength 1. Compact section (depends on width-thickness ratio) Mn = Mp = FyZ 2. Lateral-Torsional Buckling (limiting lengths Lp and Lr) - Lb ≤ Lp; no lateral-torsional buckling - Lp < Lb ≤ Lr ; - Lb > Lr ;
Design of Flexural Members Lateral-torsional buckling modification factor
Example:
Design of Flexural Members Verify the strength of the W18x50 beam, ASTM A992. Solution: Calculate the required flexural strength LRFD
ASD
Design of Flexural Members Calculate the nominal flexural strength, Mn
* moments are expressed as percentages of Mmax * Rm = 1.0 for doubly-symmetric members Check for Lateral-torsional buckling Lp = 5.83 ft < Lb = 11.7 ft < Lr = 17.0 ft
Design of Flexural Members For Lp < Lb < Lr ; = 339 kip-ft
Calculate the available flexural strength LRFD
ASD
Conclusion LRFD is becoming the predominant design philosophy • Using multiple load factors, should generally lead to some economy, particularly for low ratios of Live to Dead loads. A slight increase in cost is expected for higher ratios. • Basis for the margin of safety provided is more rational. • In ASD, concentration is shifted to limiting the maximum stresses rather than on the actual capacity of the member
Conclusion • LRFD provides a framework for handling unusual loading. Increase uncertainties in loading may be treated by modifying the load factors • On the other hand, if there are increased uncertainties in the resistance of the structure, a modified strength reduction factor may be used. • Change due to the loadings may be studied separately from those of the resistance
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