Advanced Methods of Structural Analysis

12.4 Limit Plastic Analysis of Continuous Beams 435 In the limit state, the bending moment at the point of application of forceP ...

436 12 Plastic Behavior of Structures Assume that in the limit state, the vertical displacement at the each forcePequals unity. ...

12.4 Limit Plastic Analysis of Continuous Beams 437 hinge. It is shown by solid circle; corresponding plastic moment isMy(Fig.12 ...

438 12 Plastic Behavior of Structures For this beam, the general expressions for shear and bending moment at any sectionxare Q.x ...

12.4 Limit Plastic Analysis of Continuous Beams 439 My My 1 lim l P ab 8 qliml 22 LPM LPM c K D My P My q My b A K B C D P a= 3 ...

440 12 Plastic Behavior of Structures Bending moment at the middle point of the second span caused by distributed load qand plas ...

12.5 Limit Plastic Analysis of Frames 441 For partCD qliml 32 2 DMy!qlimD 2My l 32 D 2 60 .kNm/ 22 .m^2 / D 30 kN=m; which lead ...

442 12 Plastic Behavior of Structures B 1 B 2 B 3 S J F B^3 +S+J Design diagram Fig. 12.9 Design diagram of the frame and possib ...

12.5 Limit Plastic Analysis of Frames 443 P Q= 2 P l/2 l h=l /2 A B CD K a Qlim a vert l/2 My Mvert y Mhory a Q b P b h Plim b b ...

444 12 Plastic Behavior of Structures 12.5.2 Sidesway Failure.............................................. This scheme of failu ...

Problems 445 For beam failureQlimD12M yvert l. This case is shown on the Fig.12.10e by line B, which is parallel to horizontal a ...

446 12 Plastic Behavior of Structures ab M N P Δ Fig. P12.2 Ans.PlimD2yA. 12.3.Symmetrical structure is subjected to loadPas sh ...

Problems 447 l x l P Fig. P12.5 Ans.PlimD .1C / .1 / My l 12.6.Determine the limit concentrated loadPfor beam with clamped ...

448 12 Plastic Behavior of Structures 12.9.Two-span uniform beamABCis subjected to uniformly distributed load and concentrated l ...

Chapter 13 Stability of Elastic Systems Theory of structural stability is a special branch of structural analysis. This theory e ...

450 13 Stability of Elastic Systems k P P a bde c EI=• EI=• P P k k EI=• EI=• EI EI PP 1 P EI P 2 P EI=• P EI A C B Fig. 13.1 Ty ...

13.1 Fundamental Concepts 451 Unstable equilibrium state means that if astructure under compressed load is dis- turbed from an i ...

452 13 Stability of Elastic Systems infinite number degrees of freedom. Structures presented in Fig.13.1a, b have one degree of ...

13.2 Stability of Structures with Finite Number Degrees of Freedom 453 13.2 Stability of Structures with Finite Number Degrees o ...

454 13 Stability of Elastic Systems To determine the critical load by static or energy method, first of all, we need to accept a ...