CE 154 Principles of Steel Design Unit 1 PDF

CE 154 Principles of Steel Design Unit 1 Introduction to Steel Design 1.1 Advantages of Steel as a Structural Material 1.2 Disadvantages of Steel as a Structural Material 1.3 Additional Properties of Structural Steel 1.4 T...

CE 154 Principles of Steel Design Unit 1 Introduction to Steel Design 1.1 Advantages of Steel as a Structural Material 1.2 Disadvantages of Steel as a Structural Material 1.3 Additional Properties of Structural Steel 1.4 Types of Structural Steels 1.5 Structural Shapes and Sections 1.6 Responsibilities of the Structural Designer 1.7 Review Exercises 1.8 Specifications and Building Codes 1.9 Loads 1.10 Load and Resistance Factor Design (LRFD) and Allowable Strength Design (ASD) 1.11 Load Computations for LRFD and ASD 1.12 Factor of Safety 1.13 Illustrative Problems 1.14 Review Exercises After careful study of this unit, students should be able to do the following: 1. Identify the advantages and disadvantages of structural steel as compared to other materials. 2. Identify the chemical components of different types of steel. 3. Understand the properties of steel. 4. Identify the different types and shapes of structural steels. 5. Understand the responsibilities of structural designers. 6. Understand the basis of the National Structural Code of the Philippines (NSCP). 7. Identify the different types of loads imposed to a structure. 8. Differentiate LRFD and ASD design methods. 9. Apply the load combinations provided by the NSCP. 1.1 ADVANTAGES OF STEEL AS A STRUCTURAL MATERIAL 1. High Strength ▪ The high strength of steel per unit of weight means that the weight of structures will be small. This fact is of great importance for long-span bridges, tall buildings, and structures situated on poor foundations. 2. Uniformity ▪ The properties of steel do not change appreciably with time, as do those of a reinforced-concrete structure. 3. Elasticity ▪ Steel behaves closer to design assumptions than most materials because it follows Hooke’s law up to fairly high stresses. The moments of inertia of a steel structure can be accurately calculated, while the values obtained for a reinforced-concrete structure are rather indefinite. Page 1 of 19  CE 154 Principles of Steel Design 4. Permanence ▪ Steel frames that are properly maintained will last indefinitely. Research on some of the newer steels indicates that under certain conditions no painting maintenance whatsoever will be required. 5. Ductility ▪ The property of a material by which it can withstand extensive deformation without failure under high tensile stresses is its ductility. The ductile nature of the usual structural steels enables them to yield locally at some specific points, thus preventing premature failures. 6. Toughness ▪ Structural steels are tough – that is, they have both strength and ductility. The ability of a material to absorb energy in large amounts is called toughness. 7. Addition to Existing Structures ▪ Steel structures are quite well suited to having additions made to them. New bays or even entire new wings can be added to existing steel frame buildings, and steel bridges may often be widened. 8. Ability to be fastened together by several simple connection devices, including welds and bolts. 9. Adaptation to prefabrication. 10. Speed of erection. 11. Ability to be rolled into wide variety of sizes and shapes. 12. Possible reuse after a structure is disassembled. 13. Scrap value, even though not reusable in its existing form. 1.2 DISADVANTAGES OF STEEL AS A STRUCTURAL MATERIAL 1. Corrosion ▪ Most steels are susceptible to corrosion when freely exposed to air and water, and therefore must be painted periodically. Copper is usually used as an anti-corrosion component. 2. Fireproofing Costs ▪ Although structural members are incombustible, their strength is tremendously reduced at temperatures commonly reached in fires when the other materials in a building burn. 3. Susceptible to Buckling ▪ As the length and slenderness of a compression member is increased, its danger of buckling increases. Some additional steel is needed to stiffen them so they will not buckle. 4. Fatigue ▪ Strength of steel may be reduced if it is subjected to a large number of stress reversals or even to a large number of variations of tensile stress. Fatigue problems occur only when tension is involved. 5. Brittle Fracture ▪ Under certain conditions steel may lose its ductility, and brittle fracture may occur at places of stress concentration. Fatigue-type loadings, very low temperatures, and tri- axial stress conditions can lead to brittle failure. Page 2 of 19  CE 154 Principles of Steel Design 1.3 ADDITIONAL PROPERTIES OF STRUCTURAL STEEL ✓ The characteristics of steel that are of the most interest to structural engineers can be examined by plotting the results of a tensile test. 𝑃 Δ𝐿 𝑓=𝐴 and 𝜀 = 𝐿 where 𝑓 = axial tensile stress 𝐴 = cross-sectional area 𝜀 = axial strain 𝐿 = length of specimen Δ𝐿 = change in length ✓ The relationship between stress and strain is linear up to the proportional limit (follow Hooke’s Law) ✓ A peak value, the upper yield point, is quickly reached after the proportional limit ✓ Levelling off at the lower yield point ✓ Plastic range – the stress remains constant, even though the strain continues to increase Page 3 of 19  CE 154 Principles of Steel Design ✓ Strain hardening – additional load (and stress) is required to cause additional elongation (and strain) ✓ A maximum value of stress is reached, after which the specimen begins to “neck down” as the stress decreases with increasing strain, and fracture occurs ✓ The elastic limit of the material is a stress that lies between the proportional limit and the upper yield point ✓ Elastic range – the linear portion of the diagram, the specimen can be unloaded without permanent deformation ✓ Yield point (yield strength), Fy – the proportional limit, elastic limit, and upper and lower yield points ✓ Ultimate tensile strength, Fu – the maximum value of stress that can be attained ✓ Modulus of elasticity, E – the ratio of stress to strain within the elastic range 1.4 TYPES OF STRUCTURAL STEELS 1. Plain carbon steels: mostly iron and carbon, with less than 1% carbon. 2. Low-alloy steels: iron and carbon plus other components (usually less than 5%). The additional components are primarily for increasing strength, which is accomplished at the expense of a reduction in ductility. 3. High-alloy or specialty steels: similar in composition to the low-alloy steels but with a higher percentage of the components added to iron and carbon. These steels are higher in strength than the plain carbon steels and also have some special quality, such as resistance to corrosion 1.5 STRUCTURAL SHAPES AND SECTIONS A structural member can be a rolled shape or can be built up from two or more rolled shapes or plates Hot-rolled Shapes The manufacturing process takes place in a mill, molten steel is taken from an electric arc furnace and poured into a continuous casting system where the steel solidifies but is never allowed to cool completely, and then passes through a series of rollers that squeeze the material into the desired cross-sectional shape Page 4 of 19  CE 154 Principles of Steel Design 1. W-shape ▪ Also called a wide-flange shape ▪ Consists of two parallel flanges separated by a single web and has two axes of symmetry Example: ✓ W indicates the type of shape ✓ 18 is the nominal depth (in inches) parallel to the web ✓ 50 is the weight in pounds per foot of length Page 5 of 19  CE 154 Principles of Steel Design 2. American Standard ▪ S-shape ▪ Similar to W-shape in having two parallel flanges, a single web, and two axes of symmetry ▪ The flanges of the W are wider in relation to the web than are the flanges of the S ▪ The outside and inside faces of the flanges of the W-shape are parallel, whereas the inside faces of the flanges of the S-shape slope with respect to the outside faces ▪ Formerly called an I-beam Example: ✓ S indicates the type of shape ✓ 18 is the nominal depth (in inches) parallel to the web ✓ 70 is the weight in pounds per foot of length 3. Angle Shapes ▪ Available in either equal-leg or unequal-leg Example: ✓ L indicates the type of shape ✓ The three numbers are the lengths of each of the two legs as measured from the corner, or heel, to the toe at the other end of the leg, and the thickness, which is the same for both legs ✓ Does not provide the weight per foot 4. American Standard Channel ▪ C-shape ▪ Has two flanges and a web, with only one axis of symmetry ▪ The inside faces of the flanges are sloping Example: ✓ C indicates the type of shape ✓ The first number gives the total depth in inches parallel to the web ✓ The second number gives the weight in pounds per linear foot ✓ The depth is exact rather than nominal 5. Structural Tee ▪ Produced by splitting an I-shaped member at middepth ▪ Sometimes referred to as split-tee ▪ The prefix of the designation is either WT, ST, or MT, depending on which shape is the “parent” ▪ The M-shape has two parallel flanges and a web, but it does not fit exactly into either the W or S categories Page 6 of 19  CE 154 Principles of Steel Design ▪ The HP shape, used for bearing piles, has parallel flange surfaces, approximately the same width and depth, and equal flange and web thicknesses Example: ✓ WT indicates that the section is cut from a W- shape ✓ Has a nominal depth of 18 inches and a weight of 105 pounds per foot, and is cut from a W36 x 210 6. Bars ▪ Can have circular, square, or rectangular sections ▪ The width of rectangular bars is less than 8 inches (200 mm) Example: 7. Plate ▪ The width is greater than 8 inches (200 mm) ▪ Designation is the abbreviation PL followed by the thickness in inches, the width in inches, and the length in feet and inches, e.g. PL 3/8 x 5 x 3’ – 2 ½” Example: 8. Hollow shapes ▪ Can be produced either by bending plate material into the desired shape and welding the seam or by hot-working to produce a seamless shape. The shapes are categorized as steel pipe, round HSS, and square and rectangular HSS ▪ The designation HSS is for “Hollow Structural Sections” ▪ For pipes, the designation is the outer diameter and wall thickness in inches, e.g. Pipe 5.563 x 0.500 ▪ For round HSS, they are designated by outer diameter and wall thickness, e.g. HSS 8.625 x 0.250 ▪ For square and rectangular HSS, they are designated by nominal outside dimensions and wall thickness, e.g. HSS 7 x 5 x 3/8 Cold-formed Shapes Made by bending thin sheets of carbon or low-alloy steels into almost any desired cross section Cold-working reduce ductility but increases strength Concrete floor slabs are very often cast on formed steel decks that serve as economical forms for the wet concrete and are left in place after the concrete hardens Page 7 of 19  CE 154 Principles of Steel Design Built-up Sections When special conditions such as the need for heavier members or particular cross-sectional geometries ASTM Designations Structural steel material conforming to one of the following ASTM specifications is approved for used (NSCP 501.3.1.1): 1. Hot-rolled structural shapes: ASTM A36/ A36M ASTM A529/ A529M ASTM A572/ A572M ASTM A588/ A588M ASTM A709/ A709M ASTM A913/ A913M ASTM A992/ A992M 2. Structural tubing: ASTM A500 ASTM A501 ASTM A618 ASTM A847 Page 8 of 19  CE 154 Principles of Steel Design 3. Pipe: ASTM A53/A53M, Gr. B 4. Plates: ASTM A36/ A36M ASTM A242/ A242M ASTM A283/ A283M ASTM 514/ A514M ASTM A529/ A529M ASTM A572/ A572M ASTM A588/ A588M ASTM A709/ A709M ASTM A852/ A852M ASTM A1011/ A1011M 5. Bars: ASTM A36/ A36M ASTM A529/ A529M ASTM A572/ A572M ASTM A709/ A709M 6. Sheets: ASTM A606 A1011/ A1011MSS HSLAS HSLAS-F Page 9 of 19  CE 154 Principles of Steel Design Applicable ASTM Specifications for Various Structural Shapes Steel ASTM Fy Min. Fu Applicable Shape Series Type Designation Yield Tensile HSS Stress Stress1 W M S HP C MC L Pipe (MPa) Rect. Round (MPa) A36 250 400-5502 A53 Gr. B 240 415 290 400 Gr. B 315 400 A500 315 430 Carbon Gr. C 345 430 Gr. A 250 400 A501 Gr. B 345 480 Gr. 50 345 450-690 A5293 Gr. 55 375 480-690 Gr. 42 290 415 Gr. 50 345 4504 A572 Gr. 55 375 480 Gr. 605 415 515 Gr. 655 450 550 High- Gr. I & II 3457 4807 Strength A6186 Gr. III 345 450 Low-Alloy Gr. 50 3458 4158 Gr. 60 415 515 A913 Gr. 65 450 550 Gr. 70 480 620 A992 345-4509 450g Corrosion 29010 43010 Resistant A242 31511 46011 High- 34512 48012 Strength A588 345 480 Low-Alloy A847 345 480 Preferred material specification. Other applicable material specification, the availability of which should be confirmed prior to specification. Material specification does not apply. 1.6 RESPONSIBILITIES OF THE STRUCTURAL DESIGNER 1 Minimum unless a range is shown. 2 For shapes over 630 kg/m, only the minimum of 400 MPa applies. 3 For shapes with a flange thickness less than or equal to 40 mm only. To improve weldability a maximum carbon equivalent can be specified (per ASTM Supplementary Requirement S78). If desired, maximum tensile stress of 620 MPa can be specified (per ASTM Supplementary Requirement S79). 4 If desired, maximum tensile stress of 480 MPa can be specified (per ASTM Supplementary Requirement S91). 5 For shapes with a flange thickness less than or equal to 50 mm only. 6 ASTM A618 can also be specified as corrosion resistant; see ASTM A618. 7 Minimum applies for walls nominally 20 mm thick and under. For wall thicknesses over 20 mm, F = 315 MPa and F = y u 460 MPa. 8 If desired, maximum yield stress of 450 MPa and maximum yield-to-tensile strength ratio of 0.85 can be specified (per ASTM Supplementary Requirement S75). 9 A maximum yield-to-tensile strength ratio of 0.85 and carbon equivalent formula are included as mandatory in ASTM A992. 10 For shapes with a a flange thickness greater than 50 mm only. 11 For shapes with a flange thickness greater than 40 mm and less than or equal to 50 mm only. 12 For shapes with a flange thickness less than or equal to 40 mm only. Page 10 of 19  CE 154 Principles of Steel Design the structural designer must learn to arrange and proportion the parts of structures so that they can be practically erected and will have sufficient strength and reasonable economy. 1. Safety Not only must the frame of a structure safely support the loads to which it is subjected, but it must support them in such a manner that deflections and vibrations are not so great as to frighten the occupants or to cause unsightly cracks. 2. Cost The designer needs to keep in mind the factors that can lower cost without sacrifice of strength. 3. Constructability The objective is the design of structures that can be fabricated and erected without great problems arising 1.7 REVIEW EXERCISES 1. List the three regions of a stress-strain diagram for mild or low-carbon structural steel. 2. Define the following: a. Proportional limit b. Elastic limit c. Yield stress 3. List the two methods used to produce steel shapes. 4. List four advantages of steel as a structural material. 5. What are the differences between wrought iron, steel, and cast iron? 6. What is the range of carbon percentage for mild carbon steel? 7. List four disadvantages of steel as a structural material. 8. List four types of failures for structural steel structures. Page 11 of 19  CE 154 Principles of Steel Design 1.8 Specifications and Building Codes Specifications they are written, not for the purpose of restricting engineers, but for the purpose of protecting the public the intent is that the loading used for design be the one that causes the largest stresses American Institute of Steel Construction (AISC) adopted by nearly all building codes American Association of State Highway and Transportations Officials (AASHTO) adopted by nearly all state highway and transportation departments International Building Code (IBC) was developed because of the need for a modern building code that emphasizes performance intended to provide a model set of regulations to safeguard the public in all communities National Structural Code of the Philippines (NSCP) an up-to-date structural code addressing the design and installation of structural systems through requirements emphasizing performance through various model codes/regulations, generally from the United States (American Society of Civil Engineers, ASCE), to safeguard the public health and safety nationwide establishes minimum requirements for structural systems using prescriptive and performance-based provisions Uniform Building Code (UBC) development of better building construction and greater safety to the public by uniformity in building laws 1.9 Loads ▪ The most important and most difficult task faced by the structural engineer is the accurate estimation of the loads that may be applied to a structure during its life. ▪ in general, loads are classified according to their character and duration of application 1. dead loads 2. live loads 3. environmental loads Dead Loads loads of constant magnitude that remain in one position consist of the structural frame’s own weight and other loads that are permanently attached to the frame e.g., for a steel-frame building, the frame, walls, floors, roof, plumbing, and fixtures refer to NSCP Section 204 Live Loads loads that may change in position and magnitude caused when a structure is occupied, used, and maintained refer to NSCP Section 205 generally classified as: 1. moving loads – live loads that move under their own power, such as trucks, people, and cranes Page 12 of 19  CE 154 Principles of Steel Design 2. movable loads – live loads that may be moved, such as furniture and warehouse materials can also be classified as: 1. Floor loads ▪ the minimum gravity live loads to be used for building floors are clearly specified in the NSCP 2. Traffic loads for bridges ▪ bridges are subjected to series of concentrated loads of varying magnitude caused by groups of truck or train wheels 3. Impact loads ▪ are caused by the vibration of moving or movable loads 4. Longitudinal loads ▪ stopping a train on a railroad bridge or a truck on a highway bridge causes longitudinal forces to be applied 5. Other live loads a. soil pressures – exertion of lateral earth pressures on walls or upward pressures on foundations b. hydrostatic pressures – water pressure on dams, inertia forces of large bodies of water during earthquakes, and uplift pressures on tanks and basement structures c. blast loads – caused by explosions, sonic booms, and military weapons d. thermal forces – due to changes in temperature, causing structural deformations and resulting structural forces e. centrifugal forces – those on curved bridges and caused by trucks and trains, or similar effects on roller coasters, etc. Environmental Loads caused by the environment in which a particular structure is located caused by rain, snow, wind, temperature change, and earthquakes technically, they are also live loads, but they are the result of the environment in which the structure is located; they are not all caused by gravity or operating conditions, as is typical with other live loads different types of environmental loads: 1. snow loads ▪ not considered in the Philippines 2. rain loads ▪ ponding – the result if water on a flat roof accumulates faster than it runs off 3. wind loads ▪ wind forces act as pressures on vertical windward surfaces, pressures or suction on sloping windward surfaces (depending on the slope), and suction on flat surfaces and on leeward vertical and sloping surfaces (due to the creation of negative pressures or vacuums) ▪ consider the effects of wind speed, shape and orientation of the building, terrain characteristics around the structure, importance of the buildings as to human life and welfare ▪ refer to NSCP Section 207 Page 13 of 19  CE 154 Principles of Steel Design 4. earthquake loads ▪ during an earthquake, there is an acceleration of the ground surface motion; vertical and horizontal components – the vertical component is assumed to be negligible ▪ structural analysis for the expected effects of an earthquake should include a study of the structure’s response to the ground motion caused by the earthquake ▪ in design, approximate the effects of ground motion with a set of horizontal static loads acting at each level of the structure ▪ drift – the movement or displacement of one story of a building with respect to the floor above or below ▪ refer to NSCP Section 208 1.10 Load and Resistance Factor Design (LRFD) and Allowable Strength Design (ASD) NSCP provides two acceptable methods for designing structural steel members and their connections 1. Load and Resistance Factor Design (LRFD) 2. Allowable Strength Design (ASD) both procedures are based on limit states design principles, which provide the boundaries of structural usefulness Limit State used to describe a condition at which a structure or part of a structure ceases to perform its intended function two categories: 1. strength limit states ▪ define load-carrying capacity, including excessive yielding, fracture, buckling, fatigue, and gross rigid body motion 2. serviceability limit states ▪ define performance, including deflection, cracking, slipping, vibration, and deterioration Major Differences Between LRFD and ASD 1. method used for calculating the design loads 2. use of resistance factors (𝜙 in LRFD) and safety factors (Ω in ASD) Service or Working Loads ▪ with both the LRFD procedure and the ASD procedure, expected values of the individual loads (dead, live, environmental) are estimated in the same manner Nominal Strengths ▪ the nominal strength of a member is its calculated theoretical strength, with no safety factors (Ω) or resistance factors (𝜙) applied in ▪ in LRFD, a resistance factor, usually less than 1.0, is multiplied by the nominal strength of a member, in ASD, the nominal strength is divided by a safety factor, usually greater than 1.0 Page 14 of 19  CE 154 Principles of Steel Design → to account for variations in material strength, member dimensions, and workmanship as well as the manner and consequences of failure 1.11 Load Computations for LRFD and ASD ▪ various combinations of the loads (service or working loads), which may occur at the same time, are grouped together and the largest values obtained are used for analysis and design of structures; largest load group (in ASD) or the largest linear combination of loads in a group (in LRFD) ▪ after the individual loads are estimated, the next problem is to decide the worst possible combinations of loads which might occur at the same time and which should be used in analysis and design ▪ LRFD Load Combinations possible service load groups are formed, and each service load is multiplied by a load factor, normally larger than 1.0, to account for the uncertainty of that particular load factored load – the resulting linear combination of service loads in a group, each multiplied by its respective load factor largest values determined are used to compute the moments, shears, and other forces in the structure (NSCP Section 203.3) where strength design or load and resistance factor design is used, structures and all portions thereof shall resist the most critical effects from the following combinations of factored loads: 1.4(𝐷 + 𝐹) (203 − 1) 1.2(𝐷 + 𝐹 + 𝑇) + 1.6(𝐿 + 𝐻) + 0.5(𝐿𝑟 𝑜𝑟 𝑅) (203 − 2) 1.2𝐷 + 1.6(𝐿𝑟 𝑜𝑟 𝑅) + (𝑓1 𝐿 𝑜𝑟 0.5𝑊) (203 − 3) 1.2𝐷 + 1.0𝑊 + 𝑓1 𝐿 + 0.5(𝐿𝑟 𝑜𝑟 𝑅) (203 − 4) 1.2𝐷 + 1.0𝐸 + 𝑓1 𝐿 (203 − 5) 0.9𝐷 + 1.0𝑊 + 1.6𝐻 (203 − 6) 0.9𝐷 + 1.0𝐸 + 1.6𝐻 (203 − 7) Where: f1 = 1.0 for floors in places of public assembly, for live loads in excess of 4.8 kPa, and for garage live load, or 0.5 for other live loads D = dead load E = earthquake load F = load due to fluids with well-defined pressures and maximum heights H = load due to lateral pressure of soil and water in soil L = live load, except roof live load, including any permitted live load reduction Lr = roof live load, including any permitted live load reduction R = rain load on the undeflected road T = self-straining force and effects arising from contraction or expansion resulting from temperature change, shrinkage, moisture change, creep in component materials, movement due to differential settlement, or combinations thereof Page 15 of 19  CE 154 Principles of Steel Design W = load due to wind pressure (reduction factor 𝜙)(nominal strength of a member) ≥ computed factored force in member, 𝑅𝑢 or 𝜙𝑅𝑛 ≥ 𝑅𝑢 ▪ ASD Load Combinations the service loads are generally not multiplied by load factors or safety factors loads are summed up, as is, for various combinations, and the largest values obtained are used to compute the forces in the members (NSCP 203.4) where allowable stress or allowable strength design is used, structures and all portions thereof shall resist the most critical effects resulting from the following combinations of loads: 𝐷+𝐹 (203 − 8) 𝐷+𝐻+𝐹+𝐿+𝑇 (203 − 9) 𝐷 + 𝐻 + 𝐹 + (𝐿𝑟 𝑜𝑟 𝑅) (203 − 10) 𝐷 + 𝐻 + 𝐹 + 0.75[𝐿 + 𝑇 + (𝐿𝑟 𝑜𝑟 𝑅)] (203 − 11) 𝐸 𝐷 + 𝐻 + 𝐹 + (0.6𝑊 𝑜𝑟 ) (203 − 12) 1.4 Where: D = dead load E = earthquake load F = load due to fluids with well-defined pressures and maximum heights H = load due to lateral pressure of soil and water in soil L = live load, except roof live load, including any permitted live load reduction Lr = roof live load, including any permitted live load reduction R = rain load on the undeflected road T = self-straining force and effects arising from contraction or expansion resulting from temperature change, shrinkage, moisture change, creep in component materials, movement due to differential settlement, or combinations thereof W = load due to wind pressure nominal strength of a member largest computed force in ≥ member, 𝑅 safety factor Ω 𝑢 𝑅𝑛 or ≥ 𝑅𝑎 Ω 1.12 Factor of Safety both LRFD and ASD have goals to obtain a numerical margin between resistance and load that will result in an acceptably small chance of unacceptable structural response 1.5 in general, Ω = 𝜙 where Ω = safety factor, a number usually greater than 1.0 used in ASD 𝜙 = resistance factor, a number usually less than 1.0 used in LRFD Page 16 of 19  CE 154 Principles of Steel Design 1.13 Illustrative Problems 1. The interior floor system shown has W610x551 sections spaced 2.5 m on center and is supporting a floor dead load of 2.4 kPa and a live floor load of 3.8 kPa. Determine the governing load in kN/m that each beam must support using the LRFD Method. Dead Load for the W610x551 beam: 𝑤𝐷 = 𝑠𝑒𝑙𝑓 𝑤𝑒𝑖𝑔ℎ𝑡 + 𝑓𝑙𝑜𝑜𝑟 𝑑𝑒𝑎𝑑 𝑙𝑜𝑎𝑑 𝑤𝐷 = 5.51 𝑘𝑁 ⁄𝑚 + 2.4 𝑘𝑁 ⁄𝑚2 (5 𝑚) = 17.51 𝑘𝑁 ⁄𝑚 Live Load for the W610x551 beam: 𝑤𝐿 = 𝑙𝑖𝑣𝑒 𝑓𝑙𝑜𝑜𝑟 𝑙𝑜𝑎𝑑 𝑤𝐿 = 3.8 𝑘𝑁 ⁄𝑚2 (5 𝑚) = 19 𝑘𝑁 ⁄𝑚 Load Combinations using LRFD Method: 203 − 1 𝑈 = 1.4(𝐷 + 𝐹) 𝑤𝑢 = 1.4(𝑤𝐷 + 𝑤𝐹 ) = 1.4(17.51 + 0) = 24.51 𝑘𝑁 ⁄𝑚 203 − 2 𝑈 = 1.2(𝐷 + 𝐹 + 𝑇 ) + 1.6(𝐿 + 𝐻) + 0.5(𝐿𝑟 𝑜𝑟 𝑅) 𝑤𝑢 = 1.2(𝑤𝐷 + 𝑤𝐹 + 𝑤𝑇 ) + 1.6(𝑤𝐿 + 𝑤𝐻 ) + 0.5(𝑤𝐿𝑟 𝑜𝑟 𝑤𝑅 ) 𝑤𝑢 = 1.2(17.51 + 0 + 0) + 1.6(19 + 0) + 0.5(0) 𝑤𝑢 = 240.52 𝑘𝑁 ⁄𝑚 203 − 3 𝑈 = 1.2𝐷 + 1.6(𝐿𝑟 𝑜𝑟 𝑅) + (𝑓1 𝐿 𝑜𝑟 0.5𝑊) 𝑤𝑢 = 1.2𝑤𝐷 + 1.6(𝑤𝐿𝑟 𝑜𝑟 𝑤𝑅 ) + (𝑓1 𝑤𝐿 𝑜𝑟 0.5𝑤𝑊 ) 𝑙𝑖𝑣𝑒 𝑙𝑜𝑎𝑑 = 3.8 𝑘𝑃𝑎 < 4.8 𝑘𝑃𝑎 ∴ 𝑓1 = 0.5 𝑎) 𝑤𝑢 = 1.2(17.51) + 1.6(0) + 0.5(19) = 30.51 𝑘𝑁 ⁄𝑚 𝑏) 𝑤𝑢 = 1.2(17.51) + 1.6(0) + 0.5(0) = 21.01 𝑘𝑁 ⁄𝑚 203 − 4 𝑈 = 1.2𝐷 + 1.0𝑊 + 𝑓1 𝐿 + 0.5(𝐿𝑟 𝑜𝑟 𝑅) 𝑤𝑢 = 1.2𝑤𝐷 + 1.0𝑤𝑊 + 𝑓1 𝑤𝐿 + 0.5(𝑤𝐿𝑟 𝑜𝑟 𝑤𝑅 ) 𝑤𝑢 = 1.2(17.51) + 1.0(0) + 0.5(19) + 0.5(0) = 30.51 𝑘𝑁 ⁄𝑚 Page 17 of 19  CE 154 Principles of Steel Design 203 − 5 𝑈 = 1.2𝐷 + 1.0𝐸 + 𝑓1 𝐿 𝑤𝑢 = 1.2𝑤𝐷 + 1.0𝑤𝐸 + 𝑓1 𝑤𝐿 𝑤𝑢 = 1.2(17.51) + 1.0(0) + 0.5(19) = 30.51 𝑘𝑁 ⁄𝑚 203 − 6 𝑈 = 0.9𝐷 + 1.0𝑊 + 1.6𝐻 𝑤𝑢 = 0.9𝑤𝐷 + 1.0𝑤𝑊 + 1.6𝑤𝐻 𝑤𝑢 = 0.9(17.51) + 1.0(0) + 1.6(0) = 15.76 𝑘𝑁 ⁄𝑚 203 − 7 𝑈 = 0.9𝐷 + 1.0𝐸 + 1.6𝐻 𝑤𝑢 = 0.9𝑤𝐷 + 1.0𝑤𝐸 + 1.6𝑤𝐻 𝑤𝑢 = 0.9(17.51) + 1.0(0) + 1.6(0) = 15.76 𝑘𝑁 ⁄𝑚 ∴ the governing factored load is 𝑤𝑢 = 240.52 𝑘𝑁 ⁄𝑚 to be used for design 2. A roof system with W460x60 sections spaced 3 m on center is to be used to support a dead load of 1.92 kPa; a roof live load of 1.44 kPa; and a wind load of ±1.53 kPa. Compute the governing load per linear meter using the ASD Method. Dead Load for the W460x60 beam: 𝑤𝐷 = 0.60 𝑘𝑁 ⁄𝑚 + 1.92 𝑘𝑁 ⁄𝑚2 (3 𝑚) = 6.36 𝑘𝑁 ⁄𝑚 Roof Live Load for the W460x60 beam: 𝑤𝐿𝑟 = 1.44 𝑘𝑁 ⁄𝑚2 (3 𝑚) = 4.32 𝑘𝑁 ⁄𝑚 Wind Load for the W460x60 beam: 𝑤𝑊 = ±1.53 𝑘𝑁 ⁄𝑚2 (3 𝑚) = ±4.59 𝑘𝑁 ⁄𝑚 Load Combinations using the ASD Method: 203 − 8 𝐴 =𝐷+𝐹 𝑤𝑎 = 𝑤𝐷 + 𝑤𝐹 = 6.36 + 0 = 6.36 𝑘𝑁 ⁄𝑚 203 − 9 𝐴 =𝐷+𝐻+𝐹+𝐿+𝑇 𝑤𝑎 = 𝑤𝐷 + 𝑤𝐻 + 𝑤𝐹 + 𝑤𝐿 + 𝑤𝑇 𝑤𝑎 = 6.36 + 0 + 0 + 0 + 0 + 0 = 6.36 𝑘𝑁 ⁄𝑚 203 − 10 𝐴 = 𝐷 + 𝐻 + 𝐹 + (𝐿𝑟 𝑜𝑟 𝑅) 𝑤𝑎 = 𝑤𝐷 + 𝑤𝐻 + 𝑤𝐹 + (𝑤𝐿𝑟 𝑜𝑟 𝑤𝑅 ) 𝑤𝑎 = 6.36 + 0 + 0 + 4.32 = 10.68 𝑘𝑁 ⁄𝑚 203 − 11 𝐴 = 𝐷 + 𝐻 + 𝐹 + 0.75[𝐿 + 𝑇 + (𝐿𝑟 𝑜𝑟 𝑅)] 𝑤𝑎 = 𝑤𝐷 + 𝑤𝐻 + 𝑤𝐹 + 0.75[𝑤𝐿 + 𝑤𝑇 + (𝑤𝐿𝑟 𝑜𝑟 𝑤𝑅 )] 𝑤𝑎 = 6.36 + 0 + 0 + 0.75[0 + 0 + 4.32] = 10.68 𝑘𝑁 ⁄𝑚 𝐸 203 − 12 𝐴 = 𝐷 + 𝐻 + 𝐹 + (0.6𝑊 𝑜𝑟 ) 1.4 Page 18 of 19  CE 154 Principles of Steel Design 𝑤 𝑤𝑎 = 𝑤𝐷 + 𝑤𝐻 + 𝑤𝐹 + (0.6𝑤𝑊 𝑜𝑟 1.4𝐸) 𝑎) 𝑤𝑎 = 6.36 + 0 + 0 + 0.6(4.59) = 9.11 𝑘𝑁 ⁄𝑚 𝑏) 𝑤𝑎 = 6.36 + 0 + 0 + 0.6(−4.59) = 3.61 𝑘𝑁 ⁄𝑚 ∴ the governing load is 𝑤𝑎 = 10.68 𝑘𝑁 ⁄𝑚 for design 1.14 Review Exercises 2. Determine the maximum combined loads using the recommended NSCP expressions for LRFD and ASD. a. 𝐷 = 4.80 𝑘𝑃𝑎, 𝐿 = 3.35 𝑘𝑃𝑎, 𝑅 = 0.57 𝑘𝑃𝑎, and 𝐿𝑟 = 0.96 𝑘𝑃𝑎 b. 𝐷 = 40 𝑘𝑁, 𝐿 = 22 𝑘𝑁, 𝐿𝑟 = 11 𝑘𝑁, and 𝐸 = ±29 𝑘𝑁 c. 𝐷 = 1.20 𝑘𝑃𝑎, 𝐿𝑟 = 0.96 𝑘𝑃𝑎, and 𝐿 = 1.24 𝑘𝑃𝑎 3. Structural steel beams are to be placed at 2.5 m on center under a reinforced concrete floor slab. If they are to support a service dead load D = 3.11 kPa of floor area and a service live load L = 4.80 kPa of floor area, determine the uniform load per meter which each beam must support using the LRFD and ASD method. 4. A structural steel beam supports a roof that weighs 1.20 kPa. An analysis of the loads has the following: Lr = 0.90 kPa and W = 1.15 kPa (upwards) or 0.80 kPa (downwards). If the beams are to be spaced 1.80 m in apart, determine the uniformly distributed loads per meter by which each beam should be designed using the LRFD and ASD method. Page 19 of 19