Advanced Methods of Structural Analysis

13.6 Compressed Rods with Lateral Loading 495 Differential equation of elastic curve is EI d^2 y dx^2 DM.x/; where the bending ...

496 13 Stability of Elastic Systems Each formula of system (13.37) contains of two parts. The first part takes into ac- count th ...

13.6 Compressed Rods with Lateral Loading 497 SinceQ 0 D0; M 0 D 0 ,then(13.37) become y.x/Dy 0 C 0  sinnx n C F n^3 EI .nxsi ...

498 13 Stability of Elastic Systems Let’s the compressive forcePand critical forcePcrare related as follows: PDkPcrDk 2 EI 4l^2 ...

13.6 Compressed Rods with Lateral Loading 499 13.6.3 P-Delta Analysis of the Frames.............................. Analysis of a ...

500 13 Stability of Elastic Systems each member areP 1 DN 0 CP,whereN 0 is axial force in specified member as a result of the st ...

13.6 Compressed Rods with Lateral Loading 501 for columns are ADCD5;000 .mm/ vu u u t 18  104 .N / 2  105  N mm^2  22:2 ...

502 13 Stability of Elastic Systems It is obvious thatr 12 D 0. The free-body diagram for the cross bar is presented in Fig.13.2 ...

13.6 Compressed Rods with Lateral Loading 503 13.6.4.1 Simply Supported Beam-Column The bending moment diagrams in unit and actu ...

504 13 Stability of Elastic Systems M b M d MP l a c P P Mtr F D Fl F= 1 1 ·l ab Fig. 13.27(a) Graph multiplication method for c ...

Problems 505 Ans.PcrD k 1 .l 1 Cl 2 /^2 Ck 2 l 22 l 1 Cl 2 .1C ̨/ : 13.2.Two absolutely rigid bodies.EI D1/connected by hinge at ...

506 13 Stability of Elastic Systems k j 0 P l A Fig. P13.4 Ans. tanlD l ^2 l^2 ̨C 1 ;D r P EI , ̨D EI kl 13.5.Design diagram ...

Problems 507 x k l M 0 Q 0 EI N ky 1 Fig. P13.7 Ans. tannlDnl  1  n^2 l^2 EI kl^3  ;nD r N EI 13.8.The uniform beam with over ...

508 13 Stability of Elastic Systems l 2 P k l 1 EI Fig. P13.10 Ans. sinnl 1 sinnl 2 Dnlsinnl  l 1 l 2 l^2  P kl  ;nD r P EI ...

Problems 509 13.13.Design diagram of the frames with deformable cross bar are presented in Fig. P13.13. Derive the equation for ...

510 13 Stability of Elastic Systems Ans. ˇ ˇ ˇ ˇ ' 2 . /C21:0 1:0 0:75' 1 .2/C3:5 ˇ ˇ ˇ ˇD^0 ,1ADDh r P EI I 2BD h r 4P EI ...

Problems 511 Ans. 0 D ql^3 24 EI  12 ^3  2 tan  2   ;y  l 2  D 5ql^4 384 EI  384 5^4  sec  2  1  ^2 8  I M  l ...

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Chapter 14 Dynamics of Elastic Systems Structural dynamics is a special branch of structural analysis, which studies the behavio ...

514 14 Dynamics of Elastic Systems t y T y 0 A T t y T T t y T T ab c Fig. 14.1 Types of oscillatory motions may be divided into ...