Question

For the rigid frames shown in Figures P5–5 through P5–15, determine the displacements and rotations of the nodes, the element forces, and the reactions. The values of E;A, and I to be used are listed next to each figure.

Answer 1

If a Calculate the reaction force at node Using below relation . RIE احيا Here the uniform lood is wf is w fs length of the section - is L Substityle 250 eb lft for w 20 ft for L 25 oxzo 25oo eb d substityle 250 eb IFE for w f soft for L R2 = اديدا 250 x 20 25oo eb 2 2 calculate the moment using the below Gelabion M = ادیا substitule 250 ebl ft for & roft fool 2 250 x 20 18 8333.33 eb.ft. 0 o eb. in for Determine the values for cos o f since element from Figure Cos (0) 1 cos cos (270') c 1!

1 Determine the values at element 30x log 15o (20) Li 12 I L,2 12 x 25o (20x12) 0521 2 6 I - 6 x 25o 6.25 Li 120x12) Determine general transformed global Stiffness matrix for elemented I from equation since node is fixed we have 6 I 12 Liz L LI A GI LI 10 4 I Ki-2 0521 6.25 15 o 6.25 logo

6.25 12 5000 0.0521 15 6.25 f sine for 3 Determina values for Cos o element from figur. sino sin lano) - 1 cos (270) Determine element 3 values at 6 30*10 ( 2ox 12 125 12 I 12 x 0.0521 25o (20+12) L 3² 6.25 6 I L 3 6 x 250 (2012) Determine the general transformed global stiffness matrix for element 3 from equation since hode 4 노 fixed have is K 3-4 12 6 I 13? L 3 А. 6 I 4 I 13

K 3-4 0.0521 o 6.25 15 6.25 o loo 125000 0.0521 6.25 15 6.25 Du Delermine value element a for cos eo f sino for from fig Cosco 1 cos (35 sin (360) sinco Determine values at element C 30xio ( 20x12 ܘ 12 Sood La 12 12x 25o 521 La (20X12) 6 GX250 120*12) G. 25 La

general transformed glebad element matrix for Determine Stiffness equation since hode 4 fixed have 1 A -A o GI -12I 12 I 6 I 0 2 L L2 E L K 2-3 L2 10 GI 4 GI RI 0 L -A - - 6 I 6.I -12 I L2 12I L? 2 o 2 I GI 47 L -15 o K2 - 3 o 0.0521 6.25 -0.0521 G:25 15 -0.0521 6.25 0.0521 6.25 6.25 soo o -6.25 loos 125000 15 0 -15 0 0.0521 6.25 -0.0521 6.25 6.25 TOGO -6.25 10 Soo ol -15 ol Is -0.0521 6.25 6.0521 6.25 0 6. 25 Boo - 6.25 ܘܘܘܐ

Determine Jelation. the global mateix from [k][d] equivalent system from force we get . fare 15.05 6.25 0 -15 42 F29 15.05 6-25 0.0521 G. 25 V2 ma 02 6.25 6.25 2006 이 6.25 soo fare L -15 15.05 6.25 u 3 0.0521 - 6.25 15.05 -6.25 V3 6.25 Soo 625 -6.25 2000 2 Soo 15.05 G. 25 -15 ua 15.05 6:25 0.05 216.15 Uz 100000 - 12500 6.25 6:25 20OO - 25 Soo 42 -15 0 15.05 6.25 0.0521 -625 IS.65 6.25 V3 6.25 500 6.25 6.25 2000 obtain results for displacement at node a f 3 0 42= 43 N 2 0.2625 in oo 4147 in 2321 rad 2619 in oo 4147 in oo7631 rad 2
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