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1. Introduction to Reinforced Concrete Concrete Properties: High Compressive Strength: Concrete excels at resisting crushing forces. Low Tensile Strength: Concrete is very weak in tension, cracking easily under tensile stress. This is why steel reinforcement is crucial. Modulus of Elasticity ($E_c$): Varies with concrete strength and density. Approx $E_c = 57,000 \sqrt{f_c'}$ (for normal weight concrete). Creep: Long-term deformation under sustained load. Shrinkage: Volume reduction due to drying. Stress-Strain Curve: Non-linear, parabolic-like shape up to ultimate strength, then descending. Steel Reinforcement Properties: High Tensile Strength: Steel bars provide the necessary tensile resistance. Deformed Bars: Ribs on the surface improve bond with concrete, ensuring composite action. Yield Strength ($f_y$): Common values are $40 \text{ ksi}$ and $60 \text{ ksi}$. Modulus of Elasticity ($E_s$): Approximately $29,000 \text{ ksi}$ ($200 \text{ GPa}$). Stress-Strain Curve: Typically assumed to be elastic-perfectly plastic for design purposes. Bar Sizes: Designated by numbers (e.g., #3 to #18) corresponding to nominal diameter in eighths of an inch. Advantages of Reinforced Concrete: Good fire resistance. High resistance to wind and water. Low maintenance costs. Long service life. Adaptable to various architectural shapes. Economical for many applications. Design Philosophies: Working Stress Design (WSD): Historically used (prior to 1970s). Based on elastic behavior of concrete and steel under service (unfactored) loads. Stresses kept below allowable limits to ensure safety. Did not accurately predict ultimate strength or ductile behavior. Strength Design (USD/LRFD - Ultimate Strength Design / Load and Resistance Factor Design): Current dominant method (since 1970s). Based on inelastic behavior of materials at ultimate loads. Applies load factors to service loads to get factored loads ($U$). Applies strength reduction factors ($\phi$) to nominal strengths ($M_n, V_n, P_n$) to get design strengths ($\phi M_n$). Ensures that $\phi (\text{Nominal Strength}) \ge U (\text{Factored Load})$. Provides a more consistent level of safety and accounts for ductility. ACI 318 Building Code: "Building Code Requirements for Structural Concrete" published by the American Concrete Institute (ACI). The primary standard for reinforced concrete design and construction in the United States and many other countries. Provides minimum requirements for safety and serviceability. Updated periodically (e.g., ACI 318-19 is the current version). Load Factors (from ACI 318): Multipliers applied to service loads to account for uncertainties and variations. Typical combinations include: $U = 1.4 D$ (Dead load only) $U = 1.2 D + 1.6 L$ (Dead + Live load) $U = 1.2 D + 1.6 L + 0.5 (L_r \text{ or } S \text{ or } R)$ $U = 1.2 D + 1.6 (L_r \text{ or } S \text{ or } R) + (1.0 L \text{ or } 0.5 W)$ $U = 1.2 D + 1.0 W + 1.0 L + 0.5 (L_r \text{ or } S \text{ or } R)$ $U = 0.9 D + 1.0 W$ (and others for seismic, earth pressure, etc.) $D$: Dead Load, $L$: Live Load, $L_r$: Roof Live Load, $S$: Snow Load, $R$: Rain Load, $W$: Wind Load.