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Ae1 20 21_class 1_structural models

This document contains lecture slides for a Structural Analysis course. It discusses structural models, explaining that models are simplified representations of real structures used for calculations. It covers types of supports, loads, connections and joints in structural models. It also addresses structural stability, determinacy, and calculating internal forces like axial forces, shear forces, bending moments and torsion. Examples of structural models and buildings are provided throughout for illustration.

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cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es Hipódromo de la Zarzuela. Madrid 1931. Archiches y Domínguaz. Eduardo Torroja STRUCTURAL MODELS
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es 2.- STABILITY AND STATICALLY DETERMINACY: REACTION FORCES 1.- STRUCTURAL MODELS: types of supports and connections types of loads bars geometry 5.- ASSIGNMENT 1 3.- INTERNAL FORCES: AXIAL FORCE SHEAR FORCE BENDING MOMENT TORSION 4.- TEST 0_year 19/20
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL MODELS WE DO NOTCALCULATE REAL STRUCTURES BUT MODELS OF THOSE REAL STRUCTURES
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es Shigeru Ban. Artek Milan Pavilion 2007 STRUCTURAL MODELS
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es IT IS USELESS TO CALCULATE A MODEL IF IT DOES NOT BEHAVE AS THE REAL STRUCTURE STRUCTURAL MODELS
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es Norman Foster. Renault Distribution Center 1982 WE MUST BE AWARE OF THE RELATIONSHIP BETWEEN THE MODEL AND THE REAL STRUCTURE: partial model? Ignored effects to simplify the calculations?... STRUCTURAL MODELS
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es IT IS VERY IMPORTANT TO UNDERSTAND HOW THE LOAD “TRAVELS” ALONG THE BUILDING STRUCTURAL SYSTEM and its effects EVERY LOAD SHOULD REACH THE GROUND
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es OMA. Shenzhen Stock Exchange 2013 STRUCTURAL MODELS
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es DEPENDING ON THE MOVEMENTS OR ROTATION RESTRICTIONS WE CLASSIFY THE SUPPORTS: Types of supports and connections TYPES OF SUPPORTS
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es DEPENDING ON THE MOVEMENTS OR ROTATION RESTRICTIONS WE CLASSIFY THE SUPPORTS: Types of supports and connections STRUCTURAL MODELS
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es ROLLER TYPES OF SUPPORTS
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es PINNED SUPPORT TYPES OF SUPPORTS
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es FIXED SUPPORT TYPES OF SUPPORTS
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es DEPENDING ON THE RELATIVE MOVEMENTS OR ROTATION RESTRICTIONS BETWEEN BARS, WE CLASSIFY THE JOINTS: TYPES OF INTERNAL CONNECTIONS
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es HINGES (PINNED JOINTS) cperez.eps@ceu.es federico.prietomunoz@ceu.es STRUCTURAL ANALYSIS I 2017/2018 CLASS 1 TYPES OF INTERNAL CONNECTIONS
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es RIGID (or FIXED JOINTS) STRUCTURAL ANALYSIS I 2017/2018 CLASS 1 TYPES OF INTERNAL CONNECTIONS
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es STABILITY AND DETERMINACY A SYSTEM CAN BE CONSIDERED A STRUCTURE ONLY IF IT IS IN STABLE EQUILIBRIUM STABILITY AND DETERMINACY
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es STABILITY AND DETERMINACY STABILITY AND DETERMINACY
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es 1.- STABILITY AND DETERMINACY nº unknowns nº equilibrium equations < nº unknowns nº equilibrium equations = nº unknowns nº equilibrium equations > Unstable Statically determinate Statically indeterminate STABILITY AND DETERMINACY
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es STABILITY AND DETERMINACY STATICALLY INDETERMINATE STATICALLY DETERMINATE UNSTABLE STATICALLY DETERMINATE UNSTABLE
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es INTERNAL FORCES INTERNAL FORCES ONCE WE KNOW THE EXTERNAL EQUILIBRIUM (REACTION FORCES) WE CAN CALCULATE WHAT HAPPENS “INSIDE” THE BARS OF THE SYSTEM. WE CAN CUT THE SYSTEM, ISOLATE ONE PART OF IT AND APPLY AGAIN THE EQUILIBRIUM EQUATIONS
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es INTERNAL FORCES THE FORCE IN THE DIRECTON OF THE BAR DIRECTRIX IS CALLED AXIAL FORCE
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es INTERNAL FORCES THE ROPE IS IN TENSION AND WHEN THE CHILDREN PULL IT GETS…. ¿LONGER OR SHORTER?
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es INTERNAL FORCES THE PARTHENON INTERNAL COLUMNS ARE IN COMPRESSION THEY GET…. ¿LONGER OR SHORTER?
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es INTERNAL FORCES BE CAREFUL WITH ELEMENTS UNDER COMPRESSION AND BUCKLING
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es INTERNAL FORCES IS THIS WAY OF BREAKING BREAD EASY? WHY?
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es INTERNAL FORCES THE EFFECT OF THE SHEAR FORCE IS…
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es INTERNAL FORCES WHAT HAPPENS WHEN WE APPLY A VERTICAL FORCE IN THE MIDDLE OF A BEAM?
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es INTERNAL FORCES HOW COULD YOU REDUCE DE VERTICAL DISPLACEMENT IN THE MIDDLE OF THE SPAN?
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es INTERNAL FORCES
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es INTERNAL FORCES
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es INTERNAL FORCES WHAT WOULD HAPPEN IF ALL THE PEOPLE DECIDE TO MOVE TOWARS ONE SIDE OF THE BRIDGE?
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es INTERNAL FORCES HOW COULD YOU REDUCE THE EFFECT OF TORSION?
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es INTERNAL FORCES FOR WHICH INTERNAL FORCE IS EACH OF THIS PROFILE EFFECTIVE?
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es Type of connection? Which one restrains relative rotation? Which one restrains relative movement? TEST 0
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es Type of connection? Does any of them allow movement or rotation? TEST 0
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es Type of connection? What happens with the bending moments and the end bar moments? TEST 0
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es cperez.eps@ceu.es federico.prietomunoz@ceu.es San Francisco Suspension Bridge. Built in 1937 TEST 0
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es TEST 0
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I 2017/2018 CLASS 1
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es CAN YOU TELL THE DIFFERENCE BETWEEN A SUSPENSION BRIDGE AND A CABLE-STAYED BRIDGE? TEST 0
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es Puente de Rande cable-stayed Bridge. Vigo 1973 TEST 0
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es TEST 0
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es Vigo cable-stayed Bridge
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es Chicago John Hancock Tower 1970 TEST 0
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es Chicago Lake Shore Drive Apartments. Mies van der Rohe TEST 0
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es John Hancock Center (1970): Architectural height 1128’ (344 m), 100 stories. Plan dimensions at the ground floor: 262x164’ (78,6x49,2 m). Plan dimensions at the top floor: 160x100’ (48x30 m). Chicago John Hancock Tower 1970
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es Chicago John Hancock Tower 1970
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es Miralles-Tagliabue. Santa Caterina Market. Barcelona 1997 / 2005 TEST 0
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es REMEMBER IT IS VERY IMPORTANT TO UNDERSTAND HOW THE LOAD TRAVELS ALONG THE BUILDING STRUCTURAL SYSTEM. EVERY LOAD SHOULD REACH THE GROUND
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es Santa Caterina Market (1997/2005): Central frame span: 42 m. Roof weight: 92 kp/m2. 7 concrete supports with cross section 90 cm x 90 cm. 2 post tensioned beams with spans of 12-22 m and cantilever from 4-10 m, cross section beam depth 1,2 m. Archs of 6 m height. V shaped beams average 50 m span. Wooden Arches and Ribs coming from the original market structure in a 50%. TEST 0
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es TEST 0
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es STABILITY AND DETERMINACY? CAN YOU FIND THE REACTION FORCES? WHAT’S THE EFFECT OF THE CABLE? TEST 0
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS SIMPLE TRUSSES THE CALCULATION OF DISPLACEMENTS IF WE DO NOT APPLY THE UNIT LOAD METHOD IS REALLY TIRING… TEST 0
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS TO CALCULATE THE REACTION FORCES WE CAN APPLY THE 3 EQUILIBRIUM EQUATIONS ∑Fx = 0 ∑Fy = 0 ∑M = 0 TEST 0
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS ∑Fx = 0 ∑Fy = 0 ∑M = 0
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS ONCE WE KNOW THE VALUE OF THE REACTION FORCES WE CAN CALCULATE THE INTERNAL FORCES IN EVERY BAR. METHOD OF JOINTS TEST 0
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS TEST 0
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS TEST 0
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es federico.prietomunoz@ceu.es METHOD OF JOINTS ANALYSING EVERY JOINT EQUILIBRIUM we get to know every bar internal force TEST 0
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es federico.prietomunoz@ceu.es METHOD OF JOINTS DOES THESE RESULTS MAKE SENSE? WHAT WOULD HAPPEN IF THE HORIZONTAL LOAD WAS ZERO?
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS ONCE WE KNOW THE VALUE OF THE REACTION FORCES WE CAN ALSO CALCULATE THE INTERNAL FORCES IN SOMEBARS. METHOD OF SECTIONS USEFUL FOR CHECKING TEST 0
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS ONCE WE KNOW THE VALUE OF THE REACTION FORCES WE CAN ALSO CALCULATE THE INTERNAL FORCES IN SOMEBARS. METHOD OF SECTIONS USEFUL FOR CHECKING
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS ONCE WE KNOW THE VALUE OF THE REACTION FORCES WE CAN ALSO CALCULATE THE INTERNAL FORCES IN SOMEBARS. METHOD OF SECTIONS USEFUL FOR CHECKING TEST 0
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS Only 3 unknown bars can be cut because we have 3 EQUILIBRIUM EQUATIONS to apply to each part of the system ∑Fx = 0 ∑Fy = 0 ∑M = 0
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS Only 3 unknown bars can be cut because we have 3 EQUILIBRIUM EQUATIONS to apply to each part of the system ∑Fx = 0 ∑Fy = 0 ∑M = 0 TEST 0
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS DISPLACEMENTS ONCE WE KNOW THE VALUE OF THE INTERNAL FORCES WE CAN CALCULATE THE DISPLACEMENTS
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS THE VERTICAL REACTION FORCES ARE EQUAL WHAT HAPPENS IF WE REMOVE THE HORIZONTAL LOAD? TEST 0
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS DISPLACEMENTS. UNIT LOAD METHOD REAL SYSTEM AUXILIARY SYSTEM TEST 0
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS DISPLACEMENTS. UNIT LOAD METHOD REAL SYSTEM AUXILIARY SYSTEM P* x d real = ∑(N* x ∆Lreal) TEST 0
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS DISPLACEMENTS. UNIT LOAD METHOD REAL SYSTEM AUXILIARY SYSTEM EA = 2100000 kN P* x d real = ∑(N* x ∆Lreal) 1ud x u = 1 x (3 x 4 m x 37,5 / 2100000 ) u = 0,214 mm TEST 0
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es For the Gerber beam in the figure and the given bending moment diagram, determine: 1. Value of the punctual load P (kN) 2. Value of the distributed load q (kN/m) 3. Sign and value of the vertical reaction at D, Dy (kN) 4. Sign and value of the shear force at A, VA (kN) TEST 0
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS cperez.eps@ceu.es molina.eps@ceu.es For the Gerber beam in the figure and the given shear force diagram, determine: 1. Value of the distributed load q (kN/m) 2. Value of the length L (m) 3. Sign and value of the bending moment at the middle of CD member, MCD (mkN) 4. Sign and value of the bending moment at B, MB (mkN) 5. Sign and value of the rotation at B, θB (mrad) 6. Equivalent model for the beam ABC (types of supports and external forces). TEST 0
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS GERBER BEAM BRIDGE. Kuma Village. Japan TEST 0
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS GERBER BEAM. MODEL AND DETAIL. TEST 0
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS THREE-HINGED ARCH TEST 0
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS THREE-HINGED ARCH
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS Would the diagram be very different if the hinge at C was not there? TEST 0
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS Does this reaction force values distribution make sense? TEST 0
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS For the Gerber beam in the figure and the given shear force diagram, determine: 1. Value of the distributed load q (kN/m) 2. Value of the length L (m) 3. Sign and value of the bending moment at the middle of CD member, MCD (mkN) 4. Sign and value of the bending moment at B, MB (mkN) 5. Sign and value of the rotation at B, θB (mrad) 6. Equivalent model for the beam ABC (types of supports and external forces). TEST 0
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS Would the diagram be very different if the hinge at C was not there? TEST 0
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS ASSIGNMENT 1
cperez.eps@ceu.es molina.eps@ceu.es STRUCTURAL ANALYSIS I DEGREE IN ARCHITECTURE Year 3 Term 1 STRUCTURAL MODELS TEST 0

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