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1. Identification of structures for which prestressed concrete is practical for use, 2. Specifications and building codes 3. Philosophies of design 4. Factors of safety - ASD and LRFD methods of design By the end of this lecture, students should be able to: 1. Identify and explain various types o...

1. Identification of structures for which prestressed concrete is practical for use, 2. Specifications and building codes 3. Philosophies of design 4. Factors of safety - ASD and LRFD methods of design By the end of this lecture, students should be able to: 1. Identify and explain various types of structures (e.g., bridges, high-rise buildings, parking garages 2. Assess the feasibility of using prestressed concrete in a given structural design. 3. Understand the advantages and limitations of prestressed concrete in different structural scenarios. 4. Demonstrate knowledge of relevant building codes and standards (e.g., NSCP) that govern the design and construction of concrete structures. 5. Articulate and apply different design philosophies (e.g., strength-based, serviceability based, sustainability-based) in their structural engineering projects. 6. Understand the principles of Allowable Stress Design (ASD) and Load and Resistance Factor Design (LRFD) methods. What is Prestressed Concrete?  Prestressed concrete is an advanced form of concrete that is designed to withstand greater loads and longer spans than conventional reinforced concrete.  The primary advantage of prestressed concrete is its ability to resist tensile stresses, which traditional concrete does not handle as effectively. Basic Concepts of Prestressed Concrete What is Prestressed Concrete? Prestressed concrete involves introducing internal stresses into the concrete before it is subjected to external loads. This is achieved by pre-tensioning or post-tensioning the steel reinforcement, which counteracts the tensile stresses that will develop under service loads. Why Use Prestressed Concrete? The main benefits of prestressed concrete include:  Reduced Cracking: By counteracting tensile stresses, prestressed concrete reduces the risk of cracks.  Larger Spans: It allows for longer spans and thinner slabs, reducing the need for intermediate supports.  Enhanced Durability: Improved performance under load and reduced cracking lead to enhanced durability.  Economic Efficiency: Reduces the amount of concrete and reinforcement needed, potentially lowering construction costs. Methods of Prestressing  Pre-Tensioning  Post-Tensioning Pre-Tensioning  Process: In pre-tensioning, steel cables or rods are tensioned (stretched) before the concrete is poured. The steel is anchored at both ends and is held under tension by hydraulic jacks or other means. Once the concrete has cured and reached sufficient strength, the tension is released from the steel, which then transfers a compressive force to the concrete.  Applications: Commonly used in precast concrete elements, such as beams, slabs, and panels.  Advantages Controlled Environment: Pre-tensioning is performed in a controlled environment, leading to consistent quality and accuracy. Efficient Manufacturing: It is well-suited for precast concrete products where multiple identical elements are produced.  Disadvantages Limited Flexibility: It is less flexible for cast-in-situ applications where elements are cast on-site and need to be post-tensioned. Post-Tensioning  Process: In post-tensioning, the steel cables or rods are embedded in ducts within the concrete. After the concrete has cured, the cables are tensioned using hydraulic jacks, and then the ducts are grouted to bond the cables to the concrete.  Applications: Often used in cast-in-situ concrete structures, such as slabs and large-span bridges.  Advantages Flexibility: Post-tensioning can be used for on-site construction and for structures with complex geometries. Adaptability: It allows for adjustments to the level of prestressing even after the concrete has been poured.  Disadvantages Construction Complexity: The process involves more steps, including the placement and tensioning of tendons and grouting, which can increase construction complexity and require careful quality control. Inspection and Maintenance: The grouted ducts need to be inspected and maintained to ensure long-term durability. Comparative Summary  Pre-Tensioning: o Method: Tensioning of steel before concrete placement. o Applications: Precast concrete elements. o Advantages: Controlled environment, efficient for mass production. o Disadvantages: Less flexibility for on-site adjustments.  Post-Tensioning: o Method: Tensioning of steel after concrete placement. o Applications: Cast-in-situ structures, complex shapes. o Advantages: Flexibility in design, adaptability for various applications. o Disadvantages: Increased construction complexity, requires careful grouting and inspection. Design Principles Stress and Strain in Prestressed Concrete  Initial Stress: Prestressing introduces an initial compressive stress in the concrete, which counteracts the tensile stresses imposed by external loads.  Service Loads: The design must ensure that the concrete remains in a state of compression under service loads, with tensile stresses kept within acceptable limits. Concrete and Steel Properties  Concrete: Typically, concrete is designed to resist compression. Its strength is characterized by compressive strength (e.g., 30 MPa, 40 MPa).  Steel: High-strength steel tendons or cables are used to provide tensile strength. The steel’s strength is characterized by its yield strength and ultimate tensile strength. Analysis and Design Moment-Curvature Relationship: The analysis of prestressed concrete structures involves understanding how moments and curvatures affect the stress distribution. Load Balancing: Ensure that the prestressing forces and external loads are balanced to prevent excessive deformation or failure Applications Prestressed concrete is used in various applications, including:  Bridges: Long spans and reduced depth.  Buildings: High-rise structures and large floor slabs.  Parking Structures: Efficient use of space with fewer columns.  Industrial Structures: Large spans and heavy loads. Codes and Standards Designing prestressed concrete structures involves following established codes and standards, which provide guidelines on material properties, design procedures, and safety factors. In the Philippines, standards such as the National Structural Code of the Philippines (NSCP) and American Concrete Institute (ACI) codes are used. NSCP 2015 specifications and building codes on prestressed concrete The National Structural Code of the Philippines (NSCP) 2015 includes detailed specifications and guidelines for prestressed concrete design. 1. General Requirements 1.1. Scope and Application The NSCP 2015 provides comprehensive guidelines for the design and construction of prestressed concrete structures, including both pre-tensioned and post-tensioned systems. It applies to various types of structures, including bridges, buildings, and industrial facilities. 1.2. Compliance with Standards The code refers to and incorporates principles from international standards and codes, such as the American Concrete Institute (ACI) codes, to ensure the quality and safety of prestressed concrete construction. 2. Materials 2.1. Concrete Strength: Concrete used in prestressed concrete elements must have a minimum compressive strength, typically specified in the code (e.g., 28 MPa for normal-strength concrete). Mix Design: The concrete mix must be designed to achieve the required strength and durability. Factors like water-cement ratio, aggregate quality, and admixtures are considered. 2.2. Steel Tendons Material: High-strength steel tendons (either steel strands or bars) must meet specific standards for tensile strength, ductility, and durability. Specifications: Tendons must conform to recognized standards, such as ASTM or equivalent local standards. 3. Design Requirements 3.1. General Design Principles Serviceability and Strength: The design must ensure that prestressed concrete elements can withstand service loads without excessive deformation and maintain strength under ultimate loads. Prestressing Force: The amount of prestressing force applied must be carefully calculated to ensure it effectively counters the anticipated tensile stresses. 3.2. Stress Limits Concrete Stress: The design must ensure that the compressive stress in concrete does not exceed specified limits under service conditions. Steel Stress: The stress in prestressing steel must be monitored to avoid over-stressing and to ensure safety. 3.3. Load and Resistance Factor Design (LRFD) Load Factors: The NSCP 2015 employs load and resistance factor design to account for variability in loads and material properties. Resistance Factors: The code provides factors to account for uncertainties in the strength of materials and the accuracy of design models. Design Philosophies of Prestressed Concrete The design philosophies of prestressed concrete revolve around optimizing performance by balancing stresses, ensuring serviceability, maximizing efficiency, and enhancing durability. By carefully applying these principles, engineers can create structures that are not only strong and functional but also economical and aesthetically pleasing. 1. Balancing Stresses 1.1. Pre-Tensioning and Post-Tensioning Pre-Tensioning: Steel tendons are stretched before the concrete is poured, creating an initial compressive stress in the concrete once the tension is released. This helps counteract tensile stresses that occur when the structure is in use. Post-Tensioning: Tendons are placed in ducts within cured concrete and tensioned afterward. This method allows for adjusting the prestressing force to counteract tensile stresses that develop during service. 1.2. Reducing Tension Cracking The primary philosophy is to introduce compressive stresses in the concrete that counteract the tensile stresses from external loads. This reduces or eliminates cracks and increases the durability of the structure. 2. Serviceability and Strength 2.1. Serviceability Deflection Control: The design aims to limit deflections under service loads to ensure functional performance and aesthetic quality. By controlling deflection, prestressed concrete ensures that the structure remains within acceptable limits of deformation. Crack Control: By applying prestressing forces, the design minimizes the width and occurrence of cracks, maintaining the structure's appearance and preventing damage. 2.2. Strength Ultimate Load Capacity: The design ensures that the structure can safely support maximum expected loads, including live loads, dead loads, and other forces. This involves calculating the required prestressing force to maintain safety under extreme conditions. 3. Load and Resistance Factor Design (LRFD) 3.1. Load Factors Safety Margins: The LRFD philosophy incorporates load factors to account for uncertainties in load estimations. This approach ensures that structures can handle loads beyond the nominal values with a specified level of safety. 3.2. Resistance Factors Material Strength: Resistance factors are applied to account for variations in material properties and construction practices. This ensures that the structure remains safe and reliable even with potential deviations from ideal conditions. Factors of safety - ASD and LRFD methods of design In the design of prestressed concrete structures according to the National Structural Code of the Philippines (NSCP) 2015, safety is ensured through the application of different design methodologies. The two primary methods are 1. Allowable Stress Design (ASD) and 2. Load and Resistance Factor Design (LRFD). Each method incorporates factors of safety in different ways. Allowable Stress Design (ASD)  Factors of Safety  Material Strength: In ASD, the ultimate strength of materials is divided by a safety factor to determine the allowable stress. For concrete, the compressive strength is reduced by a factor to obtain the allowable stress. For steel tendons, the yield strength is similarly divided by a safety factor. Concrete: Typically, the allowable stress in concrete is calculated by dividing the characteristic compressive strength by a safety factor, often around 0.6 to 0.75 of the design strength. Steel Tendons: The allowable tensile stress in prestressing steel is usually taken as a fraction of the ultimate tensile strength, with a safety factor of approximately 0.7 to 0.8.  Service Load Condition: ASD primarily considers service loads, which are the loads expected during the normal use of the structure. The design ensures that stresses under these loads remain within allowable limits.  Design Process Stress Calculation: Calculate the stresses induced in the concrete and steel tendons under service loads. Comparison with Allowable Stresses: Ensure that these stresses do not exceed the allowable stress values defined by the code. Safety Margins: The use of safety factors provides a margin of safety against potential variations in material properties and loading conditions. Load and Resistance Factor Design (LRFD)  Factors of Safety In LRFD, various load types (dead loads, live loads, wind loads, etc.) are multiplied by load factors to account for uncertainties in the magnitude and effects of these loads. The factors increase the nominal loads to ensure safety. Dead Load Factor: Typically, dead loads are multiplied by a load factor, often around 1.2 to 1.4. Live Load Factor: Live loads are also multiplied by a factor, usually around 1.6 to 1.8, to account for variability in occupancy and usage. Environmental Loads: Additional factors may be applied to environmental loads such as wind, seismic, and snow.  Resistance Factors: The nominal strength of materials is reduced by resistance factors to account for uncertainties in material properties and construction practices. Concrete: The nominal strength of concrete is multiplied by a resistance factor, typically around 0.65 to 0.75. Steel Tendons: The nominal tensile strength of steel tendons is reduced by a resistance factor, generally around 0.8 to 0.9.  Design Process Load Calculation: Determine the factored loads by applying appropriate load factors. Resistance Calculation: Calculate the design resistance by applying resistance factors to the nominal material strengths. Safety Assurance: Ensure that the design resistance exceeds the factored loads to maintain safety and structural integrity. Comparison of ASD and LRFD ASD Design Basis: Based on service loads and allowable stresses. Safety Factors: Applied to material strengths to determine allowable stresses. Simplicity: Generally simpler in terms of calculations and application. LRFD Design Basis: Based on factored loads and reduced resistance. Load and Resistance Factors: Applied separately to loads and material strengths. Flexibility: Provides a more refined approach to account for uncertainties and varying load conditions. Terminologies used in Prestressed Concrete Prestressing: The process of applying an initial compressive force to concrete members before they are subjected to service loads. Pre-tensioning: A method of prestressing where the tendons (steel cables or rods) are stretched and anchored before the concrete is poured and cured. Post-tensioning: A method of prestressing where the tendons are installed in ducts within the concrete after it has been cast and cured, and then stressed to apply a compressive force. Tendons: Steel cables, rods, or bars used in prestressing concrete. They are the components that are stretched and stressed to provide the compressive force. Anchorage: The device or system used to secure the ends of the tendons in both pre- tensioning and post-tensioning systems. Ducts: Tubes or channels embedded in the concrete that contain the tendons during the post-tensioning process. They protect the tendons and allow for the application of prestress. Prestressing Force: The initial force applied to the tendons during the prestressing process, which is transferred to the concrete. Release of Stress: The process of transferring the prestressing force from the tendons to the concrete, often done after the concrete has reached sufficient strength. Effective Prestress: The portion of the initial prestressing force that remains in the concrete member after accounting for losses due to factors such as elastic deformation, shrinkage, and relaxation. Losses of Prestress: The reduction in the effective prestress force over time due to factors like creep, shrinkage, relaxation of the tendons, and other effects. Concrete Creep: The gradual increase in deformation under a constant load over time, which affects the amount of prestress that is retained in the concrete. Shrinkage: The reduction in the volume of concrete as it dries and cures, affecting the prestressing force. Relaxation of Tendons: The decrease in the stress within the tendons over time due to the gradual reduction in the tension they carry. Stress Distribution: The way in which the internal forces are spread throughout the concrete member, influenced by the prestressing forces. Prestressed Concrete Beam: A beam that has been prestressed to improve its load- carrying capacity and reduce deflection. Prestressed Concrete Slab: A flat, horizontal structural element that has been prestressed, commonly used in floors and roofs. Anchorages: Devices or systems used to securely attach the ends of the tendons to the concrete structure. Bonding: The adhesion between the tendons and the surrounding concrete, which allows the transfer of stress. Strain Compatibility: The condition where the strains in the prestressed concrete member are consistent with the stress-strain relationship of both the concrete and the tendons. Stress-Bonded System: A system in which the tendons are bonded to the concrete to ensure that the prestress force is effectively transferred. REFERENCES: 1. Lin, T. Y., & Burns, N. H. (1988). Prestressed concrete. McGraw-Hill. 2. Chia, N. C. S. M. (2005). Design of prestressed concrete structures. Wiley. 3. Schuster, M. L., & Hsu, R. C. (1997). Prestressed concrete: Analysis and design. McGraw-Hill. 4. National Structural Code of the Philippines 2015 Gravity and Lateral Loads on Structures  Gravity Loads on Structures TOPICS: 1. Code provisions-NSCP C101 2. Dead load 3. Live load 4. Other gravity loads 5. Seismic Load 6. Wind Load By the end of this lecture, students should be able to: 1. Apply relevant building codes and standards (e.g., NSCP) to determine appropriate load values and load combinations for design purposes. 2. Identify and apply the different types of gravity loads that act on structures, including dead loads (permanent/static loads) and live loads. 3. Differentiate between wind loads, seismic loads, and other lateral loads, and understand their impact on structural design. 4. Calculate the magnitude of lateral loads using the formulas and guidelines provided by the NSCP 2015.  Gravity Loads on Structures The National Structural Code of the Philippines (NSCP) C101 provides guidelines related to gravity loads on structures, which are critical for ensuring the safety and stability of buildings and other structures. Gravity Loads 1. Dead Loads (DL) 2. Live Loads (LL) 3. Snow Loads 4. Wind Loads 5. Seismic Loads  Gravity Loads on Structures 1. Dead Loads (DL) Definition: Permanent loads that are static and non-variable, such as the weight of the structure itself, fixed installations, and any other permanent elements. Calculation: Must be accurately calculated based on the material properties, dimensions, and installation details of all structural components. 2. Live Loads (LL) Definition: Loads that are variable and can change in magnitude and location, such as occupants, furniture, and movable equipment. Design Considerations: Typically specified by use category (e.g., residential, office, industrial) and must account for different load combinations.  Gravity Loads on Structures 3. Snow Loads Definition: Loads due to accumulated snow on roofs and other surfaces. Factors: Considerations include geographic location, roof slope, and thermal properties of the roof. 4. Wind Loads Definition: Though primarily addressed under wind load provisions, these can indirectly affect gravity load considerations due to dynamic effects and pressure changes on the structure. 5. Seismic Loads Definition: Similar to wind loads, seismic loads are primarily covered under seismic provisions but can affect gravity load distributions during an earthquake.  Gravity Loads on Structures Load Combinations The NSCP 2015 (National Structural Code of the Philippines 2015) provides specific load combinations to ensure that structures are designed to safely withstand various types of loads. The load combinations account for different scenarios, including the simultaneous effects of different loads. Gravity Loads on Structures Gravity Loads on Structures  Gravity Loads on Structures Minimum Design Loads Load combinations for are changed due to the use of strength‐based wind loading based on ASCE 7‐10 Additional live load designations for parking, garage, and ramp live loading Basic wind speed are revised based on latest studies For communication towers, ANSI TIA/EIA 222G latest edition is fully referenced in the NSCP  Gravity Loads on Structures Near‐source factors are revised to consider distance to source 0.7 second, else Ft=0 wx: mass at floor level hx: height of floor from ground level  Lateral Loads on Structures Dynamic Analysis – Response Spectrum  Lateral Loads on Structures Load Combinations Buildings, towers and other vertical structures and all portions thereof shall be designed to resist the load combinations in NSCP Section 203. The critical effect can occur when one or more of the contributing loads are not acting. D = dead load E = earthquake load Em = estimated maximum earthquake force that can be developed in the structure F = load due to fluids with well‐defined pressures and maximum heights H = load due to lateral pressure of soil and water in soil  Lateral Loads on Structures 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 roof 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  Lateral Loads on Structures 𝑈 = 1.4 𝐷 + 𝐹 𝑈 = 1.2 (𝐷 + 𝐹 + 𝑇 ) + 1.6 (𝐿 + 𝐻) + 0.5(𝐿𝑟 𝑜𝑟 𝑅) 𝑈 = 1.2 𝐷 + 1.6 (𝐿𝑟 𝑜𝑟 𝑅) + (𝑓1𝐿 𝑜𝑟 0.50 𝑊) 𝑈 = 1.2 𝐷 + 1.0 𝑊 + 𝑓1 𝐿 + 0.5 (𝐿𝑟 𝑜𝑟 𝑅) 𝑈 = 1.2 𝐷 + 1.0 𝐸 + 𝑓1 𝐿 𝑈 = 0.9 𝐷 + 1.0 𝑊 + 1.6 𝐻 𝑈 = 0.9 𝐷 + 1.0 𝐸 + 1.6 𝐻 f1 = 1.0 for floors in places of public assembly. For live loads in excess of 4.8 kPa, and garage live load = 0.5 for other live loads  Lateral Loads on Structures Application of the strength design load combinations that involve the seismic load E for the moment resisting frame 𝑓1 = 0.5𝜌 = 1.1𝐼 = 1.0𝐶𝑎 = 0.44𝑍 = 0.4  Lateral Loads on Structures Load Combination for Strength Design Beam A‐B and Column C‐D are elements of the special moment‐ resisting frame. Structural analysis has provided the following individual beam moments at A, and the column axial loads and moments at C due to dead load, office building live load, and lateral seismic forces. Dead Load D Live Load L Lateral Seismic Load Eh Beam Moment at A 135 kN‐m 65 kN‐m 165 kN‐m Column C‐D axial load 400 kN 180 kN 490 kN Column Moment at C 55 kN‐m 30 kN‐m 220 kN‐m PROBLEM : Find the strength design moment at beam end A and strength design axial load and moment at column top C.  Lateral Loads on Structures Strength design moment at beam end A. Determine earthquake load E: The earthquake load E consists of two components as shown below in equation (208‐1). Eh is due to horizontal forces, and Ev is due to vertical forces. 𝐸 = 𝜌𝐸ℎ + 𝐸𝑣 (𝑆𝑒𝑐𝑡𝑖𝑜𝑛 208‐ 1) The moment due to vertical earthquake forces is calculated 𝑬𝒗 = 𝟎. 𝟓𝑪𝒂 𝑰𝑫 = 𝟎. 𝟓(𝟎. 𝟒𝟒)(𝟏. 𝟎)(𝟏𝟑𝟓) = 𝟐𝟗. 𝟕 𝒌𝑵‐ 𝒎 The moment due to horizontal earthquake forces is given as 𝑬𝒉 = 𝟏𝟔𝟓 𝒌𝑵‐ 𝒎 Therefore = 𝝆𝑬𝒉 + 𝑬𝒗 = 𝟏. 𝟏(𝟏𝟔𝟓) + 𝟐𝟗. 𝟕 = 𝟐𝟏𝟏 𝒌𝑵‐ 𝒎  Lateral Loads on Structures 𝑈 = 1.4 𝐷 + 𝐹 = 1.4D 𝑈 = 1.2 (𝐷 + 𝐹 + 𝑇 ) + 1.6 (𝐿 + 𝐻) + 0.5(𝐿𝑟 𝑜𝑟 𝑅) = 1.2D + 1.6L 𝑈 = 1.2 𝐷 + 1.6 𝐿𝑟 𝑜𝑟 𝑅 + 𝑓1𝐿 𝑜𝑟 0.50 𝑊 = 1.2D + 0.5L 𝑈 = 1.2 𝐷 + 1.0 𝑊 + 𝑓1 𝐿 + 0.5 (𝐿𝑟 𝑜𝑟 𝑅) = 1.2D + 0.5L 𝑈 = 1.2 𝐷 + 1.0 𝐸 + 𝑓1 𝐿 = 1.2D + 1.0E + 0.5L 𝑈 = 0.9 𝐷 + 1.0 𝑊 + 1.6 𝐻 = 0.9D 𝑈 = 0.9 𝐷 + 1.0 𝐸 + 1.6 𝐻 = 0.9D + 1.0E  Lateral Loads on Structures Apply earthquake load combinations The basic load combinations for strength design (or LRFD) are given in Section 203.3.1. For this example, the applicable equations are: 𝟏. 𝟐𝑫 + 𝟏. 𝟎𝑬 + 𝒇𝟏𝑳 (𝑺𝒆𝒄𝒕𝒊𝒐𝒏 𝟐𝟎𝟑‐ 𝟓) 𝟎. 𝟗𝑫 ± 𝟏. 𝟎𝑬 (𝑺𝒆𝒄𝒕𝒊𝒐𝒏 𝟐𝟎𝟑‐ 𝟔) Using Equation (203‐5) and Equation (203‐6), the strength design moment at A for combined dead, live, and seismic forces are determined. 𝑴𝑨 = 𝟏. 𝟐𝑴𝑫 + 𝟏. 𝟎𝑴𝑬 + 𝒇𝟏𝑴𝑳 = 𝟏. 𝟐(𝟏𝟑𝟓) + 𝟏. 𝟎(𝟐𝟏𝟏) + 𝟎. 𝟓(𝟔𝟓) = 𝟒𝟎𝟔 𝒌𝑵‐ 𝒎 𝑴𝑨 = 𝟎. 𝟗𝑴𝑫 ± 𝟏. 𝟎𝑴𝑬 = 𝟎. 𝟗 𝟏𝟑𝟓 ± 𝟏. 𝟎(𝟐𝟏𝟏) = 𝟑𝟑𝟑 𝒌𝑵‐ 𝒎 𝒐𝒓 – 𝟗𝟎 𝒌𝑵‐ 𝒎 Therefore, MA = 406 kN‐m or –90 kN‐m  Lateral Loads on Structures Apply earthquake load combinations, continuation… 𝑴𝑨 = 𝟎. 𝟗𝑴𝑫 ± 𝟏. 𝟎𝑴𝑬 = 𝟎. 𝟗 𝟏𝟑𝟓 ± 𝟏. 𝟎(𝟐𝟏𝟏) = 𝟑𝟑𝟑 𝒌𝑵‐ 𝒎 𝒐𝒓 – 𝟗𝟎 𝒌𝑵‐ 𝒎 𝑴𝑨 = 𝟏. 𝟐𝑴𝑫 + 𝟏. 𝟔𝑴𝑳 = 𝟏. 𝟐(𝟏𝟑𝟓) + 𝟏. 𝟔(𝟔𝟓) = 𝟐𝟔𝟔 𝒌𝑵‐ 𝒎 Therefore, MA = 406 kN‐m or –90 kN‐m  Lateral Loads on Structures Strength design axial load and moment at column top C. Determine Earthquake load E: 𝑬 = 𝝆𝑬𝒉 + 𝑬𝒗 where 𝑬𝒗 = 𝟎. 𝟓𝑪𝒂𝑰𝑫 = 𝟎. 𝟐𝟐𝑫 for axial load 𝑬 = 𝝆𝑬𝒉 + 𝑬𝒗 = 𝟏. 𝟏 𝟒𝟗𝟎 + 𝟎. 𝟐𝟐 𝟒𝟎𝟎 = 𝟔𝟐𝟕 𝒌𝑵 for moment 𝑬 = 𝝆𝑬𝒉 + 𝑬𝒗 = 𝟏. 𝟏(𝟐𝟐𝟎) + 𝟎. 𝟐𝟐(𝟓𝟓) = 𝟐𝟓𝟒 𝒌𝑵  Lateral Loads on Structures Apply Earthquake Load combinations: 𝟏. 𝟐𝑫 + 𝟏. 𝟎𝑬 + 𝒇𝟏𝑳 (Section 203‐5) 𝟎. 𝟗𝑫 ± 𝟏. 𝟎𝑬 (Section 203‐6) Design axial force Pc at point C is calculated as 𝑃𝑐 = 1.2𝐷 + 1.0𝐸 + 𝑓1𝐿 = 1.2(400) + 1.0(627) + 0.5(180) = 1197 𝑘𝑁 𝑃𝑐 = 0.9𝐷 ± 1.0𝐸 = 0.9 400 ± 1.0(627) = 987 𝑘𝑁‐ 𝑚 𝑜𝑟 ‐ 267 𝑘𝑁 Therefore, 𝑃𝑐 = 1197 𝑘𝑁 𝑜𝑟 – 267 𝑘𝑁  Lateral Loads on Structures Apply Earthquake Load combinations: 𝟏. 𝟐𝑫 + 𝟏. 𝟎𝑬 + 𝒇𝟏𝑳 (Section 203‐5) 𝟎. 𝟗𝑫 ± 𝟏. 𝟎𝑬 (Section 203‐6) Design axial force Pc at point C is calculated as = 987 𝑘𝑁‐ 𝑚 𝑜𝑟 ‐ 267 𝑘𝑁 = 0.9 400 ± 1.0(627)𝑃𝑐 = 0.9𝐷 ± 1.0𝐸 𝑇ℎ𝑒𝑟𝑒𝑓𝑜𝑟𝑒, 𝑃𝑐 = 1197 𝑘𝑁 𝑜𝑟 – 267 𝑘𝑁  Lateral Loads on Structures Design moment Mc at point C is calculated: 𝑻𝒉𝒆𝒓𝒆𝒇𝒐𝒓𝒆, 𝑴𝒄 = 𝟑𝟑𝟓 𝒌𝑵‐ 𝒎 𝒐𝒓 – 𝟐𝟎𝟓 𝒌𝑵‐ 𝒎 = 𝟑𝟎𝟒 𝒌𝑵‐ 𝒎 𝒐𝒓 ‐ 𝟐𝟎𝟓 𝒌𝑵‐ 𝒎 = 𝟎. 𝟗 𝟓𝟓 ± 𝟏. 𝟎(𝟐𝟓𝟒)𝑴𝒄 = 𝟎. 𝟗𝑫 ± 𝟏. 𝟎𝑬 = 𝟑𝟑𝟓 𝒌𝑵‐ 𝒎 = 𝟏. 𝟐(𝟓𝟓) + 𝟏. 𝟎(𝟐𝟓𝟒) + 𝟎. 𝟓(𝟑𝟎)𝑴𝒄 = 𝟏. 𝟐𝑫 + 𝟏. 𝟎𝑬 + 𝒇𝟏𝑳 Note that the column section capacity must be designed for the interaction of Pc = 1197 kN compression and Mc = 335 kN‐m (for dead, live and earthquake), and the interaction of Pc = 267 kN tension and Mc = ‐205 kN‐m (for dead and earthquake).  Lateral Loads on Structures Minimum Design Loads Load combinations for are changed due to the use of strength‐based wind loading based on ASCE 7‐10 Additional live load designations for parking, garage, and ramp live loading Basic wind speed are revised based on latest studies For communication towers, ANSI TIA/EIA 222G latest edition is fully referenced in the NSCP  Lateral Loads on Structures Loads and Actions Near‐source factors are revised to consider distance to source