Flexural Analysis of Beams: Properties, Advantages, Disadvantages, and Design Codes, Lecture notes of Engineering

Download Flexural Analysis of Beams: Properties, Advantages, Disadvantages, and Design Codes and more Lecture notes Engineering in PDF only on Docsity! FLEXURAL ANALYSIS OF BEAMS GROUP MEMBERS JIMMY ALEJO VERNADETH GARCILIAN PAUL ADRIAN CALUCAG ERICA FLORES CABANILLA WYNDALE MANALWAP HANNAH JOY LEGATOC FL VARGAS COLLEGE INC. ENGR. HERIBIRTH JIMENEZ PROFESSOR Concrete and Reinforced Concrete ● Concrete is a mixture of sand, gravel, crushed rock, or other aggregates held together in a rocklike mass with a paste of cement and water. ● Concrete has a high compressive strength and a very low tensile strength. ● Reinforced concrete is a combination of concrete and steel wherein the steel reinforcement provides the tensile strength lacking in the concrete. Disadvantages of Reinforced Concrete as a Structural Material ● Concrete has a very low tensile strength, requiring the use of tensile reinforcing. ● Forms are required to hold the concrete in place until it hardens sufficiently. ● The low strength per unit of weight of concrete leads to heavy members. ● The properties of concrete vary widely because of variations in its proportioning and mixing. Design codes ● AMERICAN CONCRETE INSTITUTE (ACI) ● INTERNATIONAL BUILDING CODE (IBC) ● AMERICAN ASSOCIATION OF STATE HIGHWAYS AND TRANSPORTATION OFFICIALS (AASHTO) ● NATIONAL STRUCTURAL CODE OF THE PHILIPPINES (NSCP) Properties of concrete (SECTION 419-NSCP 2015) ● The compressive strength of concrete f’c, is determined by testing the failure 28 day old 6-in. diameter by 12-in. concrete cylinders at a specified rate loading ● Although concretes are available with 28-day ultimate strengths from 2500 psi up to as high as 10,000 psi to 20,000 psi, most of the concretes used to fall into the 3000-psi to 7000- psi range. ● Specified Compressive Strength, f’c. Properties of concrete (SECTION 419-NSCP 2015) ● Modulus of Elasticity of Concrete, Ec Properties of concrete (SECTION 419-NSCP 2015) ▪Concrete has no clear cut modulus of elasticity. Its value varies different concrete strengths, concrete age, type of loading, and the characteristics and proportions of the cement and aggregates. ▪Elastic Modulus quantifies a material’s resistance to non-permanent, or elastic, deformation ▪Modulus of Rupture, fr Properties of concrete (SECTION 419-NSCP 2015) 419.2.3 Modulus of Rupture 419.2.3.1 Modulus of rupture, f,., for concrete shall be calculated by: fr = 0.62A,/f7 (419.2.3.1) where the value of A is in accordance with Section 419.2.4. 419.2.4 Lightweight Concrete 419.2.4.1 To account for the properties of lightweight concrete, a modification factor A is used as a multiplier of fe in all applicable provisions of this Code. 419.2.4,.2 The value of A shall be based on the composition of the aggregate in the concrete mixture in accordance with Table 419.2.4,2 or as permitted in Section 419.2.4.3. Table 419,2.4,2 Modification Factor Concrete Composition of aggregates a A . Fine: ASTM C330M All-lightweight Coarse: ASTM C330M 0,75 : Ri Fine: Combination of ASTM aad 330M and C33M 0.15 100.85" Coarse: ASTM C330M i % Fine; ASTM C33M Sand-lightweight Coarse: ASTM (330M 0.85 : : Fine: ASTM C33M —— a Coarse: Combination of 0.85 to 1.00"! : ASTMC330M and C33M Normal-weight Fine or Coarse: ASTM C33M 1,00 "Linear interpolation from 0.75 to 0.85 is permitted based on the absolute volume of normal weight fine aggregate as a fraction of the total absolute volume of fine aggregate.”ILinear interpolation from 0.85 to 1.00 is permitted based on the absolute volume of normal- Weight coarse aggregate as a fraction of the total absolute volume of Coarse aggregate. Steel Reinforcement (section 420 – nscp 2015) ● Bar Sizes Steel Reinforcement (section 420 – nscp 2015) ● Bar Sizes ● Commercial lengths Steel Reinforcement (Section 420 — nscp 2015) e Grades PNS ASTM Popular 49:2020 Equivalent Nomenclature Ceasar Grade 230 Grade 33 Structural Grade Lowrise Buldings and Low Loacng Conditions . Medium-rise Structures / Grade 280 Grade 40 Intermediate Grade acuriteelWiek Grade 420 Grade 60 High-Tensile Grade Medium & Highrise Structures / Infrastructure Grade 520 Grade 75 High-Tensile Grade Medium & Highrise Structures / Infrastructure i Medium & High-rise Structures / Grade 550 Grade 80 High-Tensile Grade Tafasrchrs Grades rere a) Phi Color SET cet es letere[) 230 33 . Pectler 275 40 :@ Steel Bar 415 60 ‘@ 75 “@@e 230W - "O@ Weldable 275W 0 . oe Steel Bar 415W 60 “@0@ * At both ends of the bar ** One color per end of the bar Reference: Philippine National Standard (PNS 49:2002) Loads ▪Environmental loads - Loads are caused by environment snow and ice, rain, wind, seismic loads Combination loads (Section 203 — nscp 2015) 203.2 é é ¢ Nav Wi Symbols and Notations = dead load earthquake load set forth in Section 208.6.1 = estimated maximum earthquake force that can be developed in the structure as set forth in Section 208.6.1 = lead due to fluids with well-defined pressures and maximum heights = lead due to lateral pressure of soil and water in soil = live load, except roof live load, including any permitted live load reduction = roof live load, including any permitted live load reduction ponding load rain load on the undeflected roof self-straining force and effects arising from contraction or expansion resulting from temperature change, shrinkage, moisture change, crecp in componcnt materials, movement duc to differential scttlement, or combinations thereof = load due to wind pressure Load Combinations using Strength Design or Load and Resistance Factor Design Et Basic Load Combinations re strength design or load and resistance factor design ised, structures and all portions thereof shall resist the {critical effects from the following combinations of jored loads: 1.4(D+F) (203-1) “4.2(D+F4+7)0+1.64+H) + 0.5(L, or R) (203-2) 1.2D41.6(L, or R)+UfyLor0.5W) (203-3) 1.2D+1.0W + f,L + 0.5(4, or R) (203-4) L.2D + 1.0E + fyb (203-5) 0.90 +1.0W+1.6H (203-6) 0.9D+1.0£+1.6H (203-7) 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  .2 Other Loads Vitere P is to be considered in design, the applicable load shall be added to Section 203.3.1 factored as 1.2P. 2034 Load Combinations Using Allowable Stress or Allowable Strength Design 2034.1 Basic Load Combinations Where allowable stress or allowable strength design is ‘used, structures and all portions thereof shall resist the most peal effects resulting from the following combinations loads: D+F (203-8) +H+PELeT (203-9) D+ H+F + (Lor) (203-10) — D+ N+F +0.75[L+T(L, or R)} (203-11) D+H+F+(0.6Wor a) (203-12) Combination loads (Section 203 — nscp 2015) 203.5 Special Seismic Load Combinations For both allowable stress design and strength design for concrete, and Load and Resistance Factor Design (LRED) and Allowable Strength Design (ASD) for steel, the following special load combinations for seismic design shall be used as specifically required by Section 208, or by Chapters 3 through 7. 12D +f,L+1,0B, (20319) 0.9D+ 1.06, (203-20) Flexural Analysis of Beams €-in compression Jf-in compression J (This term is defined €, for steel in tension A in Section 23.) €,in tension fytension in concrete strains stresses FIGURE 21 Uncracked concrete stage. Flexural Analysis of Beams Concrete Cracked–Elastic Stresses Stage - Mcr known cracking moment - tensile stress at the bottom Equals modulus of rupture - the compression stress at the top is less than 0.5f'c -steel stress is less than yield stress Flexural Analysis of Beams Concrete Cracked—Elastic Stresses Stage PoP 6 oe SA M., mM, @ fc Se <s eee b—— strains stresses (b) FIGURE 22 Concrete cracked—elastic stresses stage. Flexural Analysis of Beams When failure occurs, concrete is crushed here. €- concrete _ compressive stress ol poe Sy - strains (steel stresses has yielded) FIGURE 2.3. Ultimate-strength stage. Flexural Analysis of Beams failure Myiors reinforcing bars yield ~—__ approximate service or working load range —+ Moment tensile concrete cracks —- Curvature, 6 FIGURE 2.4 Moment—curvature diagram for reinforced concrete beam with tensile reinforcing only. Beam Concepts and Derivation εt = fy/Es Strain Diagram Stress Diagram As