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changes.mady.by.user Zeynep Aladağ

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changes.mady.by.user oğuzcan hadim

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Ab

Mathinline
body--uriencoded--$$ \normalsize A_b = \dfrac%7B \pi d%5e2%7D %7B4%7D = \dfrac%7B \pi 20%5e2%7D %7B4%7D = 314.159\; \mathrm%7Bmm%5e2%7D $$

Fn

Mathinline
body--uriencoded--$$ \normalsize F_n = 0.450 F_%7Bub%7D = 0.450 \times 1000 =450\; \mathrm%7BN/mm%5e2%7D $$

Rn

Mathinline
body--uriencoded--$$ \normalsize R_n = F_n A_b = 4 \times 450 \times 314.159 \times 10%5e%7B-3%7D = 565.486 \; \mathrm%7BkN%7D $$

AISC 360-16 J3-1

ΦRn

Mathinline
body--uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 565.486 = 424.115 \; \mathrm%7BkN%7D $$

Required

Available

Ratio

Control

413.063 kN

424.115 kN

0.974

√

...

dh

20+2=22 mm

 

Lc,edge

Mathinline
body--uriencoded--$$ \normalsize L_%7Bc,edge%7D = L_e - 0.5d_h = 40 - 0.5 \times 22 =29\; \mathrm%7Bmm%7D $$

 

Rn

Mathinline
body--uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 1.2L_c \times t \times F_u \\2.4d \times t \times F_u \end%7Bmatrix%7D\right] \end%7Baligned%7D

AISC 360-16 J3-6a

Rn-edge

Mathinline
body--uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 1.2(29)(16)(469.999 470 \times 10%5e%7B-3%7D) \\2.4(20)(16)(469.999 470 \times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D =261.696\; \mathrm%7BkN%7D

 

Lc,spacing

Mathinline
body--uriencoded--$$ \normalsize L_%7Bc,spacing%7D = s - d_h = 60 - 22 = 38\; \mathrm%7Bmm%7D $$

 

Rn-spacing

Mathinline
body--uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 1.2(38)(16)(469.999 470 \times 10%5e%7B-3%7D) \\2.4(20)(16)(469.999 470 \times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D =342.912\; \mathrm%7BkN%7D

 

Rn

Mathinline
body--uriencoded--$$ \normalsize R_%7Bn%7D = n_eR_%7Bn,edge%7D + n_sR_%7Bn,spacing%7D $$

Mathinline
body--uriencoded--$$ \normalsize R_%7Bn%7D = 2 \times 261.696 + 2 \times 342.912 = 1209.216 \; \mathrm%7BkN%7D $$

 

ΦRn

Mathinline
body$$ --uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 1209.216 = 906.912 \; \mathrm%7BkN%7D $$

 

Required

Available

Ratio

Control

413.063 kN

906.912 kN

0.455

√

...

dh

20+2=22 mm

 

Lc,edge

Mathinline
body--uriencoded--$$ \normalsize L_%7Bc,edge%7D = L_e - 0.5d_h = 40 - 0.5 \times 22 =29 \; \mathrm%7Bmm%7D $$

 

Rn

Mathinline
body--uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 1.2L_c \times t \times F_u \\2.4d \times t \times F_u \end%7Bmatrix%7D\right] \end%7Baligned%7D

AISC 360-16 J3-6a

Rn-edge

Mathinline
body--uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 1.2(29)(10)(469.999 470 \times 10%5e%7B-3%7D) \\2.4(20)(10)(469.999 470 \times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D =163.559\; \mathrm%7BkN%7D

 

Lc,spacing

Mathinline
body--uriencoded--$$ \normalsize L_%7Bc,spacing%7D = s - d_h = 60 - 22 = 38\; \mathrm%7Bmm%7D $$

 

Rn-spacing

Mathinline
body--uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 1.2(38)(10)(469.999 470 \times 10%5e%7B-3%7D) \\2.4(20)(10)(469.999 470 \times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D = 214.32 \; \mathrm%7BkN%7D

 

Rn

Mathinline
body--uriencoded--$$ \normalsize R_%7Bn%7D = n_eR_%7Bn,edge%7D + n_sR_%7Bn,spacing%7D $$

Mathinline
body--uriencoded--$$ \normalsize R_%7Bn%7D = 2 \times 163.559 + 2 \times 214.32 = 755.758 \; \mathrm%7BkN%7D $$

 

ΦRn

Mathinline
body--uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 755.758 = 566.82 \; \mathrm%7BkN%7D $$

 

Required

Available

Ratio

Control

413.063 kN

566.82 kN

0.729

√

...

Fe

490000 kN/m2

w

5.658 mm

Fu-plate

469.999  N/mm2

Fu-brace

410 N/mm2

tplate

16 mm

tbrace

10 mm

Rnw

Mathinline
body--uriencoded--$$ \normalsize R_%7Bnw%7D = 0.6 \times F_e \times 2 \times 0.707 \times w $$

Mathinline
body--uriencoded--$$ \normalsize R_%7Bnw%7D = 0.6 \times 490 \times 2 \times 2 \times 0.707 \times 5.658 =4704 \; \mathrm%7BkN/m%7D $$

Rn-plate

Mathinline
body--uriencoded--$$ \normalsize R_%7Bn,plate%7D = 0.6 F_u t l = 0.6 \times 2 \times 469.999 \times 16 =9024 $$\; \mathrm%7BkN/m%7D $$

Rn-brace

Mathinline
body--uriencoded--$$ \normalsize R_%7Bn,brace%7D = 0.6 F_u t l = 0.6 \times 4 \times 410 \times 9.3 = 9151.2\; \mathrm%7BkN/m%7D $$

RnBM

Mathinline
body--uriencoded--$$ \normalsize R_%7BnBM%7D = \mathrm%7Bmin%7D ( R_%7Bn,plate%7D , R_%7Bn,brace%7D ) =9024\; \mathrm%7BkN/m%7D $$

Rn

Mathinline
body--uriencoded--$$ \normalsize R_%7Bn%7D = \mathrm%7Bmin%7D ( R_%7Bnw%7D , R_%7BnBM%7D )l =4704 \times 140 \times 10%5e%7B-3%7D =658.56\; \mathrm%7BkN%7D $$

ΦRn

Mathinline
body--uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 658.56 = 493.92 \; \mathrm%7BkN%7D $$

Required

Available

Ratio

Control

413.063 kN

493.92 kN

0.836

√

...

K

0.65

 

L

159.85 mm

 

r

2.887 mm

 

KL / r

35.99

 

Fy

355 N/mm2

 

Ag

1892.82 mm2

 

Fe

Mathinline
body--uriencoded--$$ \normalsize F_e = \dfrac%7B \pi%5e2 E%7D %7B \left ( \dfrac%7B KL%7D %7Br%7D \right)%5e2%7D = 1523692.915 \; \mathrm%7BkN/m%5e2%7D $$

AISC 360-16 E3-4 

 

Mathinline
body--uriencoded--$$ \normalsize \dfrac%7B L_c%7D %7Bi%7D \leq 4.71 \sqrt %7B\dfrac%7BE%7D%7BF_y%7D %7D $$

 

Mathinline
body--uriencoded--$$ \normalsize 34.56 \leq 4.71 \sqrt %7B\dfrac%7B 2 \times 10%5e8%7D%7B355000%7D %7D =111.8 $$

 

Fcr

Mathinline
body--uriencoded--$$ \normalsize F_%7Bcr%7D = \left[ 0.658%5e%7B\dfrac%7BF_y%7D%7BF_e%7D%7D \right ] F_y = 322.016 \; \mathrm%7BN/mm%5e2%7D $$

AISC 360-16 E3-2 

Rn

Mathinline
body--uriencoded--$$ \normalsize R_n = F_%7Bcr%7D A_g = 322.016 \times 1892.82 \times 10%5e%7B-3%7D = 609.52 \; \mathrm%7BkN%7D $$

 AISC 360-16 E3-1 

ΦRn

Mathinline
body--uriencoded--$$ \normalsize \varphi R_n = 0.9 \times 609.52 = 548.567 \; \mathrm%7BkN%7D $$

 

Required

Available

Ratio

Control

413.063 kN

548.567 kN

0.753

√

...

K

0.65

 

L

60 mm

 

r

4.619 mm

 

KL / r

8.44

 

Fy

355 N/mm2

 

Ag

3195.199 mm2

 

Rn

Mathinline
body--uriencoded--$$ \normalsize R_n = F_%7By%7D A_%7Bg%7D (KL / r \leq 25 ) = 355 \times 3195.199 \times 10%5e%7B-3%7D = 1134.3 $$\; \mathrm%7BkN%7D $$

AISC 360-16 J4-6

ΦRn

Mathinline
body--uriencoded--$$ \normalsize \varphi R_n = 0.9 \times 1134.3 = 1020.866\; \mathrm%7BkN%7D $$

 

Required

Available

Ratio

Control

413.063 kN

1020.866 kN

0.405

√

...

Fy

355 N/mm2

Zg

Mathinline
body--uriencoded--$$ \normalsize Z_g = \dfrac%7B t_%7Bgl%7D - g%5e2 %7D %7B 4%7D = 333500.966 $$

Fa

Mathinline
body--uriencoded--$$ \normalsize F_a = N/ ( t_g l_g ) = 292.08 / ( 10 \times 365.24 ) = 79969.3\; \mathrm%7BkN/m%5e2%7D $$

N

260,207 kN

M

10.775 kNm

tg

10 mm

lg

365.24 mm

Fb

Mathinline
body--uriencoded--$$ \normalsize F_b = M/ Z_g = 12.095 / 333500.966 = 36267.78 \; \mathrm%7BkN/m%5e2%7D $$

Fn

Mathinline
body--uriencoded--$$ \normalsize F_n = F_a + F_b = 116237.092 \; \mathrm%7BkN/m%5e2%7D $$

Rn

Mathinline
body--uriencoded--$$ \normalsize R_n = F_y = 355000 \; \mathrm%7BkN/m%5e2%7D $$

ΦRn

Mathinline
body--uriencoded--$$ \normalsize \varphi R_n = 0.90 \times 355000 = 319500 \; \mathrm%7BkN/m%5e2%7D $$

Required

Available

Ratio

Control

116237.092 kN/m2

319500 kN/m2

0.364

√

...

Fy

355 N/mm2

V

292.079 kN

tg

10 mm

lg

365.24 mm

Fv

Mathinline
body--uriencoded--$$ \normalsize F_v = V/ (t_g l_g ) = 292.079/ ( 10 \times 365.24 ) = 79969.06 \; \mathrm%7BkN/m%5e2%7D $$

Rn

Mathinline
body--uriencoded--$$ \normalsize R_n = 0.6 F_y = 0.6 \times 355000 = 213000 $$\; \mathrm%7BkN/m%5e2%7D$$

ΦRn

Mathinline
body--uriencoded--$$ \normalsize \varphi R_n = 1.0 \times 355000 = 355000 \; \mathrm%7BkN/m%5e2%7D $$

Required

Available

Ratio

Control

79969.139 kN/m2

213000 kN/m2

0.375

√

...

Fpeak

Mathinline
body--uriencoded--$$ \normalsize F_%7Bpeak%7D = t_g \sqrt%7B (F_a + F_b)%5e2 + F_v%5e2 %7D $$
Mathinline
body--uriencoded--$$ \normalsize F_%7Bpeak%7D = 10 \sqrt%7B (79969.307 + 36267.786)%5e2 + 79969.139%5e2 %7D $$
Mathinline
body--uriencoded--$$ \normalsize F_%7Bpeak%7D = 1410.891 \; \mathrm%7BkN/m%7D $$

 

Favg

Mathinline
body--uriencoded--$$ \normalsize F_%7Bavg%7D = \dfrac %7B t_g \sqrt%7B (F_a - F_b)%5e2 + F_v%5e2%7D + \sqrt%7B (F_a + F_b)%5e2 + F_v%5e2 %7D %7D%7B 2 %7D =1161.101\; \mathrm%7BkN/m%7D $$

 

Rreq

Mathinline
body--uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 3231.396 = 2423.547\; \mathrm%7BkN/m%7D $$

AISC 360-16 J2-4

tg

10 mm

 

w

5.658 mm

 

Fe

490000 kN/m2

 

θ

55.473 °

 

Rn

Mathinline
body--uriencoded--$$ \normalsize R_n = 2 \times 0.707 w \times 0.6 F_E (1 + 0.5 sin (\phi)%5e%7B1.5%7D ) = 3231.396\; \mathrm%7BkN/m%7D $$

 

ΦRn

Mathinline
body--uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 3231.396 = 2423.547 \; \mathrm%7BkN/m%7D $$

 

Required

Available

Ratio

Control

1451.376 kN/m

2423.547 kN/m

0.599

√

...