Basic Structural Concepts (NSCP Based ASD to LRFD Design of Steel Structures)

BASIC STRUCTURAL CONCEPTS

NSCP Based ASD to LRFD Design of Steel Structures

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:

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) f_a ≤ F_a/FS Allowable Strength Design (ASD)

R_a ≤ R_n/

Ω

Load and Resistance Factor Design (LRFD) R_u ≤

φ

R_n

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

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, ΩΩΩΩ, 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, φφφφ.

• 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 + (L_r or R) 4. D + H + F + 0.75[L + T + (L_r 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 P_s,equiv equals the algebraic sum of D and L: P_s,equiv = D + L

• The controlling ASD load combination equation in this case is:

Comparing LRFD and ASD Load

Combinations

•

We can now determine the equivalent total load

allowed by ASD by using the design inequality:

P

_s,equiv

≤ P

_n

/

Ω

P

_s,equiv

≤ P

_n

/ 1.67 = 0.60P

_n

P

_s,equiv

/ P

_n

≤ 0.60

Comparing LRFD and ASD Load

Combinations

• The controlling LRFD load combination equation in this case is:

P_u = 1.2D + 1.6L

• We make the following definitions:

D = (X%)P_s,equiv and L = (1-X%)P_s.equiv

• Where X is the percentage of P_s,equiv that is dead load. Substituting into the load combination:

P_u = 1.2(X)P_s,equiv + 1.6(1-X)P_s,equiv = [1.6 – 0.4X]_Ps,equiv

Comparing LRFD and ASD Load

Combinations

• Substituting the above expression into the LRFD version of the design inequality, we get:

P_u ≤ P_n

[1.6 = 0,4X]P_s,equiv ≤

φ

P_n

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:

T_u ≤ φ_tT_n

Where: T_u = LRFD factored loads

T_n = nominal tensile yielding strength of the member = F_yA_g or F_uA_e

φ_t = 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

φ_t = 0.90 (LRFD); Ω_t = 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

Design of Tension Members

• Calculate the required tensile strength

LRFD ASD

Tu = 1.2(30 kips) + 1.6(90 kips)

T_u= 180 kips

Ta = 30 kips + 90 kips)

Design for Tension Members

• Check tensile yield limit state

• Check tensile rupture strength

• Check slenderness limit

L/r = (25.0 ft/1.26 in)(12.0 in/ft) = 238 < 300 LRFD ASD φtTn = (0.9)(50 ksi)(6.16 in 2 ) 277 kips > 180 kips Tn /Ω= (50 ksi)(6.16 in 2 )/1.67 184 kips > 120 kips LRFD ASD φtTn = (0.75)(65 ksi)(4.32 in 2 ) 211 kips > 180 kips Tn /Ω= (65 ksi)(4.32 in 2 )/2.00 141 kips > 120 kips

Design of Compression Members

• General Form:

P_u ≤ φ_cP_n

Where: P_u = LRFD factored loads

P_n = nominal compressive strength of the member = F_crA_g ; F_cr = flexural buckling stress

φ_c = 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 = π 2 E/(KL/r)2

= Euler Critical Buckling Stress Q = 1 for compact and non-compact sections Q = Q_sQ_a for slender sections

Design for Compression Members

Example:

Calculate the strength of W14x90 Solution:

Governing = 58.6

Design of Compression Members

Calculate flexural buckling stress:

Since ;

Design of Flexural Members

• General Form:

M_u ≤ φ_bM_n

Where: M_u = LRFD factored loads

M_n = 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) M_n = M_p = F_yZ

2. Lateral-Torsional Buckling (limiting lengths L_p and L_r) - L_b

≤

L_p; no lateral-torsional buckling

- L_p < L_b

≤

L_r ; - L_b > L_r ;

Design of Flexural Members

Lateral-torsional buckling modification factor

Design of Flexural Members

Verify the strength of the W18x50 beam, ASTM A992. Solution:

Calculate the required flexural strength

Design of Flexural Members

Calculate the nominal flexural strength, M_n

* moments are expressed as percentages of M_max * R_m = 1.0 for doubly-symmetric members

Check for Lateral-torsional buckling

Design of Flexural Members

For L_p < L_b < L_r;

= 339 kip-ft

Calculate the available flexural strength

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