Z9Z_E.RTF

Deflections

Deflections are calculated for characteristic loads (*TylkoObcDlug long-duration (for deflection without axial force, additionally including influence of short loads))*|*Long-duration and short-duration*).

Factors depending on duration of loads and conditions of environment: nk = 0,5; nd = $nid$; k = $kapa$.

$MomentyKD$

Moment diagram for short-and long-duration loads.

$MomentyD$

Moment diagram for long-duration loads.

(*TylkoObcDlug

$Strefy$

*|* Rigiditys for short-lasting influence of  all loads:

$Strefy_kd_k$

Rigiditys for short-lasting influence of long-duration loads:

$Strefy_d_k$

Rigiditys for long-lasting influence of long-duration loads:

$Strefy_d_d$*)

$Ugiecia$

Deflections.

Deflection in co-ordinated point  x = $x$ cm, calculated by integration of curvature’s function of member’s axis (1/r) , equals:

f = (*TylkoObcDlug fd(d)*|*fk(k+d) - fk(d) + fd(d) = $fkd_k$ - $fd_k$ + $fd_d$*) = $f$ mm

f = $WSGU$ = fdop

<*Strefa Rigidity in sector:              xa = $xa$   xb = $xb$ cm

Bending moment :                                          Mmax = $Mmax$ kNm

(*SilaOsiowa Axial force:                                                                      Nm = $Nm$ kN;  e = $e$ cm

*)(*TylkoObcDlug (*Zginanie Full load bending moment:              Mkd = $Mkd$ kNm

*)*)b  = $bb$ cm;                ho = h - a = $h$ - $a$ = $ho$ cm;

Fa = $Fa$ cm2;                Fac = $Fac$ cm2;

d1 = $d1$;                d2 = $d2$;                Wfp = $Wfp$ cm3                Mfp = $Mfp$ kNm

(*SilaOsiowa Nf = $Nf$ kN

*)(*Zginanie aa = (0,001 + ma) / ma = (0,001 + $mi_a$) / $mi_a$ = $alfa_$

it is accepted aa = $alfa_a$

*)(*TylkoObcDlug Rigidity for long-lasting influence of long-duration loads:

$Sztywnosc_d_d$

(*Bkd_d Rigidity for long-lasting influence of all loads:

$Sztywnosc_kd_d$

Rigidity for long-duration loads regarding short-duration loads:

              B = (Bd + Bkd) / 2 = ($Bd$+$Bkd$) / 2 = $Bsr$

*)(*Balfa_d Rigidity for moment aa Mfp  in long-duration activity:

$Sztywnosc_alfa_d$

Rigidity for long-duration loads regarding short-duration loads:

              B = (Bd + Ba) / 2 = ($Bd$+$Bkd$) / 2 = $Bsr$

*)*|*(*Bkd_k $Sztywnosc_kd_k$

*)(*Bd_k $Sztywnosc_d_k$

*)(*Bd_d $Sztywnosc_d_d$*)*)

*>             

<*Sztywnosc (*Zginanie M = $Z5-2$ = 0,8 Mfp                M = $Z5-3$ = aa Mfp*|*|Ma| = $Z5-23$ = Ma f*)

Section is working in stage $faza$.

(*Faza_Ia_II  g’a = $ga$                g’b = $gb$                G = $G$                L(*SilaOsiowa a*) = $L$

According to formulas Z5-13, Z5-10 i Z5-9 we obtain:

              x f(*SilaOsiowa a*) = $ksi_f$;                Fbc = $Fbc$ cm2;                zf = $zf$ cm

(*SilaOsiowa               Ma = $Ma$ kNm;                Mc = $Mc$ kNm;                M’f = $M_f$ kNm

*)(*Zginanie ya = 1,3 - d f aa Mfp / M = 1,3 - $df$×$alfa_a$×$Mfp$/$|M|$ = $psi_a1$*|* ya = 1,3 - d f M’f / Mc - (1- M’f / Mc) / (6 - 4,5 M’f / Mc) = 1,3 - $df$×$|M_f|$/$|Mc|$ - (1-$|M_f|$/$|Mc|$) / (6 - 4,5×$|M_f|$/$|Mc|$) = $psi_a2$*)

it is accepted ya = $psi_a$

BII = zf h0 / [ya / (Ea Fa) + 0,9 / (n Eb Fbc)] = $zf$×$ho$ / [$psi_a$ / ($Ea$×$Fa$) + 0,9 / ($ni$×$Eb$×$Fbc$)] ×10-5 = $BII$ MNm2

*)(*Faza_Ia  BI = Eb Ip(*DzialDlug / (1+k)*) = $Eb$×$Ip$(*DzialDlug  / (1+$kapa$)*) ×10-3 = $BI$ MNm2

BI a = BI [ 1 - ( 1- BII / BI ) (M - 0,8 Mfp) / (Mfp (a a - 0,8))] = $BI$× [ 1 - ( 1- $BII$ / $BI$ ) × ($|M|$ - 0,8×$Mfp$) / ( $Mfp$×($alfa_a$ - 0,8))] = $BIa$ MNm2

*)(*Faza_I  BI = Eb Ip(*DzialDlug / (1+k)*) = $Eb$×$Ip$(*DzialDlug  / (1+$kapa$)*) ×10-3 = $BI$ MNm2*)

*>