Structure tructure Analysis nalysis Structure Design Against Static Load 1. Introduction to Structure .................................................................................................... 3.1 – 3.2 2. Determinacy and Indeterminacy

Structure tructure Analysis nalysis Structure Design Against Static Load 1. Introduction to Structure .................................................................................................... 3.1 – 3.2 2. Determinacy and Indeterminacy ......................................................................................... . 3.3 – 3.12 3. Influence Line Diagram ........................................................................................................ 3.13 – 3.21 4. Moment Distribution Method ............................................................................................. 3.22 – 3.31 5. Plastic Analysis .................................................................................................................... 3.32 – 3.45 6. Arches & Cables .................................................................................................................. 3.46 – 3.54 STRUCTURE ANALYSIS INDEX GATE-O-PEDIA CIVIL ENGINEERING GATE WALLAH CIVIL HANDBOOK Design Against Static Load 3.1 1 INTRODUCTION TO STRUCTURE 1.1. Structure An elastic body is termed as structure when it provides resistance against deformation due to the load acting over it. 1.1.1. Mechanism In a mechanism no resistance is setup against deformation. Assumption • Elastic body • Homogenous • Isotropic • Continuous Solid Structure • Principal of Super position is valid. Validity of Super position Principle • Displacement is small. • Elastic material and linear structural response. Load vs deformation is a straight line. • Suppose are unyielding. • Not valid for sender columns. 1.1.2. Classification of Structures • Skeletal — e.g., Roof truss, building frames. • Surface — e.g., Slabs and shells • Solid — e.g., massive foundation Skeletal Structure • Pin Jointed : develop axial forces, external load @ joint, members are straight. • Rigid Jointed: Angle between the member meeting @ joint remain unchanged, Resist external forces by developing bending moment, shear force, axial force, twisting moments. GATE WALLAH CIVIL HANDBOOK Structure Analysis 3.2 Plane Frame Space Frame All member and forces are in one plane. All members don’t lie on one plane. Axial Axial Shear Biaxial Shear Bending Moment Biaxial Moment Twisting Moment 1.1.3. Poissons Ratio () Defined as the ratio of lateral strain to linear strain. Concrete = 0.15 Steel = 0.33 Cork = 0 Isotropic material = 0.25 max = 0.5 Ideal Elastic incompressible meter. Bernoulli's Assumption A plane section which are normal to the neutral axis before bending remain plane even after bending. It means strain varies linearly over the cross-section. Validity of Bernoulli's • Valid for elastic, limit, ultimate theories. • Valid for prismatic and non-prismatic. • Valid for shallow beams. 1.2. Reaction Reaction is the resistance against deformation. Numbers (Planar Structure) • Free end 0 • Roller end 1 • Hinged Support 2 • Fixed Support 3 • Shear hinged – Horizontal & Vertical 2 • Damper Horizontal Release  GATE WALLAH CIVIL HANDBOOK Structure Analysis 3.3 2 DETERMINACY AND INDETERMINACY The structure that can be analysed by the equations of static equilibrium alone. 2.1. Equation of Static Equilibrium 2D Planar structure  Fx = 0  Fy = 0  M = 0 3D Space Structure  Fx = 0  mx = 0  Fy = 0  my = 0  Fz = 0  mz = 0 Statically indeterminate structure are the one which cannot be found by equations of static equilibrium. 2.1.1. Degree of Static Indeterminacy Can be termed as equations in addition to static equilibrium equation required to completely analyse the structure. DS = Number of unknown forces in member or at support – equation of static equilibrium available. 2.1.2. Support Reaction Plane – Fix Rx, Ry, Mz Reactions x, y, z Restrains – Pin Rx, Ry, Reactions x, y, Restrains – Roller Ry Reactions y Restrains DS = DSi + DSe Total Internal Externa