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Old Version 19

changes.mady.by.user Zeynep Aladağ

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New Version 20

changes.mady.by.user oğuzcan hadim

Saved on

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...

Ab

Mathinline
body--uriencoded--$$ \normalsize A_%7Bb%7D = \dfrac %7B \pi d%5e2%7D%7B4%7D = \dfrac %7B \pi 24%5e2%7D%7B4%7D =452.389 $$\; \mathrm%7Bmm%5e2%7D$$

AISC 360-16 J3-1

Fn

Mathinline
body--uriencoded--$$ \normalsize F_n = 0.450F_%7Bub%7D = 0.450 \times 800 = 360 \; \mathrm%7BN/mm%5e2%7D $$

Rn

Mathinline
body--uriencoded--$$ \normalsize R_n = F_%7Bn%7DA_b = 6 \times 360 \times 452.389 \times 10%5e%7B-3%7D = 977.16 $$\; \mathrm%7BkN%7D$$

ΦRn

Mathinline
body--uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 977.16 = 732.87 \; \mathrm%7BkN%7D $$

Required

Ready

Rate

Control

425.018 kN

732.87 kN

0.580

√

...

dh

24+3=27 mm

 

Lc,edge

Mathinline
body--uriencoded--$$ \normalsize L_%7Bc,edge%7D = L_e - 0.5d_h = 75 - 0.5 \times 27 = 61.5 $$\; \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(61.5)(15)(360 \times 10%5e%7B-3%7D) \\2.4(24)(15)(360 \times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D =311.04\; \mathrm%7BkN%7D

 

Lc,spacing

Mathinline
body--uriencoded--$$ \normalsize L_%7Bc,spacing%7D = 72 - 27 = 45 $$\; \mathrm%7Bmm%7D$$

 

Rn-spacing

Mathinline
body--uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 1.2(45)(15)(360 \times 10%5e%7B-3%7D) \\2.4(24)(15)(360 \times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D =291.6\; \mathrm%7BkN%7D

 

Rn

Mathinline
body--uriencoded--$$ \normalsize R_n = n_e R_%7Bn-edge%7D + n_s R_%7Bn-spacing%7D $$
Mathinline
body--uriencoded--$$ \normalsize R_n = 2 \times 311.04 + 4 \times 291.6 = 1788.48 \; \mathrm%7BkN%7D $$

 

ΦRn

Mathinline
body--uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 1788.48 = 1341.36\; \mathrm%7BkN%7D $$

 

Required

Available

Ratio

Control

425.018 kN

1341.36 kN

0.317

√

...

dh

24+3=27 mm

 

Lc,edge

Mathinline
body--uriencoded--$$ \normalsize L_%7Bc,edge%7D = L_e - 0.5d_h = 75 - 0.5 \times 27 = 61.5 \; \mathrm%7Bmm%7D $$

 

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(61.5)(14.6)(360 \times 10%5e%7B-3%7D) \\2.4(24)(14.6)(360 \times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D =302.746\; \mathrm%7BkN%7D

 

Lc,spacing

Mathinline
body--uriencoded--$$ \normalsize L_%7Bc,spacing%7D = 72 - 27 = 45\; \mathrm%7Bmm%7D $$

 

Rn-spacing

Mathinline
body--uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 1.2(45)(14.6)(360 \times 10%5e%7B-3%7D) \\2.4(24)(14.6)(360 \times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D =283.824\; \mathrm%7BkN%7D

 

Rn

Mathinline
body--uriencoded--$$ \normalsize R_n = n_e R_%7Bn-edge%7D + n_s R_%7Bn-spacing%7D $$

Mathinline
body--uriencoded--$$ \normalsize R_n = 2 \times 302.746 + 4 \times 283.824 = 1740.788 \; \mathrm%7BkN%7D $$

 

ΦRn

Mathinline
body--uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 1740.788 = 1305.591 \; \mathrm%7BkN%7D $$

 

Required

Available

Ratio

Control

418.114 kN

1305.591 kN

0.320

√

...

Ag

Mathinline
body--uriencoded--$$ \normalsize A_%7Bg%7D = h_p \times t_ p = 180 \times 15 =2700 $$\; \mathrm%7Bmm%5e2%7D$$

 

Fy

235 N/mm2

 

Rn

Mathinline
body--uriencoded--$$ \normalsize R_n = F_%7By%7DA_g = 235 \times 2700 \times 10%5e%7B-3%7D = 634.5 $$\; \mathrm%7BkN%7D$$

AISC 360-16 J4-1

ΦRn

Mathinline
body--uriencoded--$$ \normalsize \varphi R_n = 0.9 \times 634.5 = 571.05 \; \mathrm%7BkN%7D $$

Required

Available

Ratio

Control

301.881 kN

571.92 kN

0.529

√

...

The limit state of the flange plate tension rupture is checked according to AISC 360-16.

An

Mathinline
body--uriencoded--$$ \normalsize A_n = 15( 180 - 2 \times (24 + 3 + 2 ) ) = 1830 \; \mathrm%7Bmm%5e2%7D $$

 

Ae

Mathinline
body--uriencoded--$$ \normalsize A_e = A_n \times U = 1830 \times 1 = 1830 \; \mathrm%7Bmm%5e2%7D $$

 

Fu

360 N/mm2

 

U

1.00

 

Rn

Mathinline
body--uriencoded--$$ \normalsize R_n = F_%7Bu%7DA_e = 360 \times 1830 \times 10%5e%7B-3%7D = 658.8 \; \mathrm%7BkN%7D $$

AISC 360-16 J4-2

ΦRn

Mathinline
body--uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 658.8 = 494.1 \; \mathrm%7BkN%7D $$

 

Required

Available

Ratio

Control

301.881 kN

494.1 kN

0.611

√

...

Ag

Mathinline
body--uriencoded--$$ \normalsize A_%7Bg%7D = 15 ( 4 \times 72 + 2 \times 75 ) =6570 \; \; \mathrm%7Bmm%5e2%7D $$

 

Anv

Mathinline
body--uriencoded--$$ \normalsize A_%7Bnv%7D = 6570 - 2 ( 2.5 \times 29 \times 15 ) =4395 \; \mathrm%7Bmm%5e2%7D $$

 

Ant

Mathinline
body--uriencoded--$$ \normalsize A_%7Bnt%7D = 15 \times 2( 35 - 0.5 \times 29 ) =615 $$\; \mathrm%7Bmm%5e2%7D$$

 

Fy

235 N/mm2

 

Fu

360 N/mm2

 

Ubs

1.0

 

 

Mathinline
body--uriencoded--$$ \normalsize U_%7Bbs%7D F_u A_%7Bnt%7D = 1 \times 360 \times 10%5e%7B-3%7D \times 615 = 221.4\; \mathrm%7BkN%7D $$

Mathinline
body--uriencoded--$$ \normalsize 0.6 F_%7Bu%7D A_%7Bnv%7D = 0.6 \times 360 \times 10%5e%7B-3%7D \times 4470 = 965.52 $$\; \mathrm%7BkN%7D$$

Mathinline
body--uriencoded--$$ \normalsize 0.6 F_%7By%7D A_%7Bg%7D = 0.6 \times 235 \times 10%5e%7B-3%7D \times 6570 = 926.37\; \mathrm%7BkN%7D $$

 

Rn

Mathinline
body--uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 0.6F_uA_%7Bnv%7D \\0.6F_yA_%7Bg%7D \end%7Bmatrix%7D\right] \end%7Baligned%7D + U_%7Bbs%7DF_uA_%7Bnt%7D
Mathinline
body--uriencoded-- \normalsize R_n =926.37+221.4=1147.77.77\; \mathrm%7BkN%7D

AISC 360-16 J4-5

ΦRn

Mathinline
body--uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 1147.77 = 860.8275 \; \mathrm%7BkN%7D $$

 

Required

Available

Ratio

Control

301.881 kN

860.828 kN

0.351

√

...

Ag

Mathinline
body--uriencoded--$$ \normalsize A_%7Bg%7D = 14.6 \times ( 588 - 2 \times 75 ) =6394.8 \; \mathrm%7Bmm%5e2%7D $$

 

Anv

Mathinline
body--uriencoded--$$ \normalsize A_%7Bnv%7D = 6570 - 2 \times ( 2.5 \times 29 \times 15 ) =4395 \; \mathrm%7Bmm%5e2%7D $$

 

Ant

Mathinline
body--uriencoded--$$ \normalsize A_%7Bnt%7D = 14.6 \times 2( 35 - 0.5 \times 29 ) =598.6 \; \mathrm%7Bmm%5e2%7D $$

 

Fy

235 N/mm2

 

Fu

360 N/mm2

 

Ubs

1.0

 

 

Mathinline
body--uriencoded--$$ \normalsize U_%7Bbs%7D F_u A_%7Bnt%7D = 1 \times 360 \times 10%5e%7B-3%7D \times 598.6 = 215.496 $$\; \mathrm%7BkN%7D$$

Mathinline
body--uriencoded--$$ \normalsize 0.6 F_%7Bu%7D A_%7Bnv%7D = 0.6 \times 360 \times 10%5e%7B-3%7D \times 4277.8 = 924 $$\; \mathrm%7BkN%7D$$

Mathinline
body--uriencoded--$$ \normalsize 0.6 F_%7By%7D A_%7Bg%7D = 0.6 \times 235 \times 10%5e%7B-3%7D \times 6394.8 = 901.66 $$\; \mathrm%7BkN%7D$$

 

Rn

Mathinline
body--uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 0.6F_uA_%7Bnv%7D \\0.6F_yA_%7Bg%7D \end%7Bmatrix%7D\right] \end%7Baligned%7D + U_%7Bbs%7DF_uA_%7Bnt%7D

Mathinline
body--uriencoded--$$ R_n =901.66 + 215.496 = 1117.156\; \mathrm%7BkN%7D $$

AISC 360-16 J4-5

ΦRn

Mathinline
body--uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 1117.77 = 837.867 $$\; \mathrm%7BkN%7D$$

 

Required

Available

Ratio

Control

301.881 kN

837.867 kN

0.360

√

...

K

0.65

 

L

150 mm

 

r

4.33 mm

 

KL / r

22.52

 

Fy

235 N/mm2

 

Ag

Mathinline
body--uriencoded--$$ \normalsize A_%7Bg%7D = h_p \times t_ p = 180 \times 15 =2700 \; \mathrm%7Bmm%5e2%7D $$

 

Rn

Mathinline
body--uriencoded--$$ \normalsize R_n = F_%7By%7DA_%7Bg%7D (KL/r) = 235 \times 10%5e%7B-3%7D \times 2700 = 634.5\; \mathrm%7BkN%7D $$

AISC 360-16 J4-6

ΦRn

Mathinline
body--uriencoded--$$ \normalsize \varphi R_n = 0.9 \times 634.5 = 571.05 $$\; \mathrm%7BkN%7D$$

 

Required

Available

Ratio

Control

418.114 kN

571.05 kN

0.732

√

...

Ab

Mathinline
body--uriencoded--$$ \normalsize A_b = \dfrac%7B \pi d%5e2%7D %7B4%7D = \dfrac%7B \pi 24%5e2%7D %7B4%7D = 452.389 \; \mathrm%7Bmm%5e2%7D $$

Fn

Mathinline
body--uriencoded--$$ \normalsize F_n = 0.450 F_%7Bub%7D = 0.450 \times 800 = 360 \; \mathrm%7BN/mm%5e2%7D $$

Rn

Mathinline
body--uriencoded--$$ \normalsize R_n = F_n A_b = 2 \times 360 \times 452.389 \times 10%5e%7B-3%7D = 325.72\; \mathrm%7BkN%7D $$

AISC 360-16 J3-1

ΦRn

Mathinline
body--uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 325.72 = 244.29\; \mathrm%7BkN%7D $$

Required

Available

Ratio

Control

0.031 kN

244.29 kN

0.00013

√

...

dh

24+3=27 mm

 

Lc,edge

Mathinline
body--uriencoded--$$ \normalsize L_%7Bc,edge%7D = L_e - 0.5d_h = 49.5 - 0.5 \times 27 =36\; \mathrm%7Bmm%7D $$

 

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(36)(10)(360 \times 10%5e%7B-3%7D) \\2.4(24)(10)(360 \times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D =155.52\; \mathrm%7BkN%7D

 

Rn

Mathinline
body--uriencoded--$$ \normalsize R_%7Bn%7D = n_eR_%7Bn,edge%7D =2 \times 155.52 =311.04\; \mathrm%7BkN%7D $$

 

ΦRn

Mathinline
body--uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 311.04 = 233.28\; \mathrm%7BkN%7D $$

 

Required

Available

Ratio

Control

0.031 kN

233.28 kN

0.0001

√

...

dh

24+3=27 mm

 

Lc,edge

Mathinline
body--uriencoded--$$ \normalsize L_%7Bc,edge%7D = L_e - 0.5d_h = 55 - 0.5 \times 27 =41.5\; \mathrm%7Bmm%7D $$

 

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(41.5)(9.4)(360 \times 10%5e%7B-3%7D) \\2.4(24)(9.4)(360 \times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D = 168.52\; \mathrm%7BkN%7D

 

Rn

Mathinline
body--uriencoded--$$ \normalsize R_%7Bn%7D = n_eR_%7Bn,edge%7D =1 \times 168.52 =168.52\; \mathrm%7BkN%7D $$

 

ΦRn

Mathinline
body--uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 168.52 = 126.39 $$\; \mathrm%7BkN%7D$$

 

Required

Available

Ratio

Control

0.031 kN

126.392 kN

0.00024

√

...

Ag

Mathinline
body--uriencoded--$$ \normalsize A_%7Bg%7D = h_p \times t_ p = 2 \times 325 \times 10 =6500 $$\; \mathrm%7Bmm%5e2%7D$$

 

Fy

235 N/mm2

 

Rn

Mathinline
body--uriencoded--$$ \normalsize R_n = 0.6F_%7By%7DA_g = 0.6 \times 235 \times 10%5e%7B-3%7D \times 6500 = 916.5 .5 \; \mathrm%7BkN%7D $$

AISC 360-16 J4-3

ΦRn

Mathinline
body--uriencoded--$$ \normalsize \varphi R_n = 1 \times 916.5 = 916.5 $$\; \mathrm%7BkN%7D$$

 

Required

Available

Ratio

Control

0.075 kN

916.5 kN

0.0001

√

...

Anv

Mathinline
body--uriencoded--$$ \normalsize A_%7Bg%7D = 2\times 10 \times ( 325 -3 \times (24 + 3 + 2 ) ) =4760 \; \mathrm%7Bmm%5e2%7D $$

 

Ae

Mathinline
body--uriencoded--$$ \normalsize A_%7Be%7D = A_n \times U = 4760 \times 1 = 4760 \; \mathrm%7Bmm%5e2%7D $$

 

Fu

360 N/mm2

 

Rn

Mathinline
body--uriencoded--$$ \normalsize R_n = F_%7Bu%7DA_%7Be%7D = 0.6 \times 360 \times 4760 \times 10%5e%7B-3%7D = 1028.16\; \mathrm%7BkN%7D $$

AISC 360-16 J4-4

ΦRn

Mathinline
body--uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 1028.16 = 771.12 $$\; \mathrm%7BkN%7D$$

 

Required

Available

Ratio

Control

0.075 kN

771.12 kN

0.0001

√

...

Ag

Mathinline
body--uriencoded--$$ \normalsize A_%7Bg%7D = 2\times 10 \times ( 325 -49.5 ) =5510 $$\; \mathrm%7Bmm%5e2%7D$$

 

Anv

Mathinline
body--uriencoded--$$ \normalsize A_%7Bnv%7D = 5510 - 2 \times ( 2.5 \times 29 \times 10 ) =4060 $$\; \mathrm%7Bmm%5e2%7D$$

 

Ant

Mathinline
body--uriencoded--$$ \normalsize A_%7Bnt%7D = 10 \times 2 \times ( 55 - 0.5 \times 29 ) = 810 $$\; \mathrm%7Bmm%5e2%7D$$

 

Fy

235 N/mm2

 

Fu

360 N/mm2

 

Ubs

1.0

 

 

Mathinline
body--uriencoded--$$ \normalsize U_%7Bbs%7D F_u A_%7Bnt%7D = 1 \times 360 \times 10%5e%7B-3%7D \times 810 = 291.6 $$

Mathinline
body--uriencoded--$$ \normalsize 0.6 F_%7Bu%7D A_%7Bnv%7D = 0.6 \times 360 \times 10%5e%7B-3%7D \times 4060 = 876.96 $$

Mathinline
body--uriencoded--$$ \normalsize 0.6 F_%7By%7D A_%7Bg%7D = 0.6 \times 235 \times 10%5e%7B-3%7D \times 5510 = 776.91 $$

 

Rn

Mathinline
body--uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 0.6F_uA_%7Bnv%7D \\0.6F_yA_%7Bg%7D \end%7Bmatrix%7D\right] \end%7Baligned%7D + U_%7Bbs%7DF_uA_%7Bnt%7D
Mathinline
body--uriencoded--R_n = 776.91 + 291.6 =1068.51\; \mathrm%7BkN%7D

AISC 360-16 J4-5

ΦRn

Mathinline
body--uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 1068.51 = 801.38\; \mathrm%7BkN%7D $$

 

Required

Available

Ratio

Control

0.075 kN

801.38 kN

0.0001

√

...