mathcad - foss equestrian stables - andre.pdf

Foss Equestrian Stables - Andre - 2015-03-24.xmcd__________________________________________________________________________________________________

Page 1 of 103/25/2015

Foss Equestrian Stables - Andre Loading loading according to

NBC

dl_roof 0.8kPa:= dl_roof 0.8 kPa=

sl_roof 1kPa:= sl_roof 1 kPa=

sl_unb 1.25 sl_roof:= sl_unb 1.25 kPa=

deadload

1)

2)

3)

4)

5)

6)

Steel Deck 1.22mm

200mm Insulation

15mm Plywood

Joists

Membrane

Misc

dl_1 130Pa:= dl_1 0.13 kPa=

dl_2 0.5Pamm

200 mm:= dl_2 0.1 kPa=

dl_3 5Pamm

15 mm:= dl_3 0.075 kPa=

dl_4 100Pa:= dl_4 0.1 kPa=

dl_5 100Pa:= dl_5 0.1 kPa=

dl_6 200Pa:= dl_6 0.2 kPa=

_________________________________________________________________________________

Total _dl dl_1 dl_2+ dl_3+ dl_4+ dl_5+ dl_6+:= _dl 0.705 kPa=

snowload: s_s 1.1kPa:= s_r 0.1kPa:= roofslope _roof atan 4.512

20.556 deg=:=

c_b 0.8:= c_s 1.0 _roof 30degif

:=

c_w 1.0:=

c_a 1.0:= c_s 1=

sl_roof_check s_s c_b c_w c_a c_s s_r+ 0.98 kPa=:=


Page 2 of 103/25/2015

windload: q_50 0.6kPa:= h_reference 6.4m:=

c_e max 0.9h_reference

10m

0.2,

:= c_e 0.915= for open terrain

Windload based on I-7, Case A, 20 deg, Surface 1, 2, 3 & 4

Wall windward S1 cpcg_ext 1.05:= cp_int 0.45:= cg_int 2:=

WL_1_S1 q_50 c_e cpcg_ext cp_int cg_int( ):= WL_1_S1 1.07 kPa=

Roof windward S2 cpcg_ext 1.3:=


Roof leeward S1 cpcg_ext 0.9:=

WL_1_S3 q_50 c_e cpcg_ext cp_int cg_int( ):= WL_1_S3 0 kPa=

Wall leeward S1 cpcg_ext 0.8:=


Wall windward S1 cpcg_ext 1.05:= cp_int 0.3:= cg_int 2:=


Roof windward S2 cpcg_ext 1.3:=


Roof leeward S1 cpcg_ext 0.9:=


Wall leeward S1 cpcg_ext 0.8:=



Page 3 of 103/25/2015

Loadcombinations

LC1: dl + sl (dl = 1.25, sl = 1.50)

LC2: dl + sl unb (dl = 1.25, sl = 1.50)LC3: dl + wl 1 (dl = 0.90, wl = 1.40) not

usedfor semi-circle

LC4: dl + wl 2 (dl = 0.90, wl = 1.40)LC5: dl + sl + wl 1 (dl = 1.25, sl = 1.50, wl = 0.40)LC6: dl + sl + wl 2 (dl = 1.25, sl = 1.50, wl = 0.40)LC7: dl + sl unb + wl 1 (dl = 1.25, sl = 1.50, wl = 0.40)LC8: dl + sl unb + wl 2 (dl = 1.25, sl = 1.50, wl = 0.40)LC9: dl + wl 1 + sl (dl = 1.25, wl = 1.40, sl = 0.50)LC10: dl + wl 2 + sl (dl = 1.25, wl = 1.40, sl = 0.50)LC11: dl + wl 1 + sl unb (dl = 1.25, wl = 1.40, sl = 0.50)LC12: dl + wl 2 + sl unb (dl = 1.25, wl = 1.40, sl = 0.50)

General InformationSpecies: D.Fir --> q_r 6.44MPa:= --> p_r 24.2MPa:=

Steel: --> res_stl 0.9 300 N

mm2

:=res_stl 270 MPa=


Page 4 of 103/25/2015

Roof over Riding CircleTudor Arch Loading

TA1 LC1: w_Beam 175mm:= l_Beam 90ft 912mm+ 28.344 m=:=d_Beam 988mm:= trib_width 6.5m 6.5 m=:=

dl_B1_LC1 dl_roof trib_width sin 77deg( ):= dl_B1_LC1 5.067 kNm

=

dl_B1_LC1 dl_roof trib_width sin 77deg( ) 45

:= dl_B1_LC1 4.053 kNm

=


:= dl_B1_LC1 3.04 kNm

=


:= dl_B1_LC1 2.027 kNm

=


:= dl_B1_LC1 1.013 kNm

=

sl_B1_LC1 sl_roof trib_width sin 77deg( ):= sl_B1_LC1 6.333 kNm

=

sl_B1_LC1 sl_roof trib_width sin 77deg( ) 45

:= sl_B1_LC1 5.067 kNm

=


:= sl_B1_LC1 3.8 kNm

=


:= sl_B1_LC1 2.533 kNm

=


:= sl_B1_LC1 1.267 kNm

=

trib_width 5.9m 5.9 m=:=

dl_B1_LC1 dl_roof trib_width:= dl_B1_LC1 4.72 kNm

=

sl_B1_LC1 sl_roof trib_width:= sl_B1_LC1 5.9 kNm

=

Check S-Frame

Area_ground 555619068mm2:=

R_dl Area_ground 0.8 kPa 1.5 666.743 kN=:= R_sframe_dl 806kN:=

R_sl Area_ground 1 kPa 555.619 kN=:= R_sframe_dl 693kN:=

R_LC1 1.25 R_dl 1.5 R_sl+ 1.667 103 kN=:= R_sframe_LC1 2047kN:=

S-Frame loading conservative


Page 5 of 103/25/2015

TA - Lower TP - LC1 (Semicircle SFrame 4.0)compressive force C_f_LC1 391kN:=

max Moment - Strong Axis X M_f_X_LC1 320kN m:= (negative bending - compression at bottom)

Moment Resistance - Strong Axis X - LC1 k_d 1.0:= k_sb 0.8:=w_Beam 315mm:=

K_X 1 200019

3000

2:= K_X 0.92=d_Beam 988mm:=

E_Beam 12400MPa:= for D.Fir 20f-EXa_uns 8m:= unsupported length

f_b 25.6MPa:= L_M0 8m:= length between Moment = 0

M_r1 F_b S_Beam K_X K_ZBG:= K_ZBG 0.919= M_r1 799 kN m=

M_r2 F_b S_Beam K_X K_L:= K_L 0.972= M_r2 845 kN m=

M_r_X min M_r1 M_r2, ( ):=M_r_X 799 kN m= > M_f_X_LC1 320 kN m=

Compressive Resistance - par to grain - LC1 k_d 1.0:= k_ct 0.75:= (k_ct = 0.75 for wet service)

l_Beam 16.6m:= sys_c1 0:= C_c1 l_Beam sys_c1w_Beam

:= C_c1 0=

E_Beam 12400MPa:= for D.Fir 20f-EX sys_c2 1:= C_c2 l_Beam sys_c2d_Beam

:= C_c2 16.802=

f_cb 30.2MPa:=

C_r f_cb k_d k_ct A_Beam K_Zcg K_C:= K_Zcg 0.549= K_C 0.828=

C_r 2563 kN= > C_f_LC1 391 kN=

LC1: C_f_LC1C_r

M_f_X_LC1M_r_X

+ 55.314 %= < 100 %

E_05_Beam 0.87 E_Beam:=

k_se 0.8:= P_epi

2 E_05_Beam k_sew_Beam d_Beam3

12

1.0 l_Beam sys_c2( )27.826 103 kN=:=

LC1: C_f_LC1C_r

2 M_f_X_LC1M_r_X

1

1C_f_LC1

P_e

+ 44.494 %= < 100 %


Page 6 of 103/25/2015

TA - Haunch - LC1

compressive force C_f_LC1 475kN:=



K_X 1 200019

3000

2:= K_X 0.92=d_Beam 1786mm:=








:= C_c1 0=


:= C_c2 9.295=

f_cb 30.2MPa:=


C_r 5021 kN= > C_f_LC1 475 kN=

LC1: C_f_LC1C_r

M_f_X_LC1M_r_X

+ 39.304 %= < 100 %


k_se 0.8:= P_epi


12

1.0 l_Beam sys_c2( )24.623 104 kN=:=

LC1: C_f_LC1C_r

2 M_f_X_LC1M_r_X

1

1C_f_LC1

P_e

+ 31.048 %= < 100 %


Page 7 of 103/25/2015

TA - Upper TP - LC1




K_X 1 200019

3000

2:= K_X 0.92=d_Beam 988mm:=








:= C_c1 0=


:= C_c2 16.802=

f_cb 30.2MPa:=


C_r 2563 kN= > C_f_LC1 471 kN=

LC1: C_f_LC1C_r

M_f_X_LC1M_r_X

+ 96.492 %= < 100 %


k_se 0.8:= P_epi


12

1.0 l_Beam sys_c2( )27.826 103 kN=:=

LC1: C_f_LC1C_r

2 M_f_X_LC1M_r_X

1

1C_f_LC1

P_e

+ 86.497 %= < 100 %


Page 8 of 103/25/2015

TA - Mid Rafter - LC2


max Moment - Strong Axis X M_f_X_LC2 75kN m:= (positive bending - compression at top)


K_X 1 200019

3000

2:= K_X 0.92=d_Beam 817mm:=




M_r2 F_b S_Beam K_X K_L:= K_L 1= M_r2 594 kN m=




:= C_c1 0=

E_Beam 12400MPa:= for D.Fir 20f-E sys_c2 1:= C_c2 l_Beam sys_c2d_Beam

:= C_c2 20.318=

f_cb 30.2MPa:=


C_r 1906 kN= > C_f_LC2 348 kN=

LC2: C_f_LC2C_r

M_f_X_LC2M_r_X

+ 33.032 %= < 100 %


k_se 0.8:= P_epi


12

1.0 l_Beam sys_c2( )24.425 103 kN=:=

LC2: C_f_LC2C_r

2 M_f_X_LC2M_r_X

1

1C_f_LC2

P_e

+ 19.366 %= < 100 %


Page 9 of 103/25/2015

TA - Mid Rafter - LC2




K_X 1 200019

3000

2:= K_X 0.92=d_Beam 817mm:=




M_r2 F_b S_Beam K_X K_L:= K_L 1= M_r2 330 kN m=




:= C_c1 0=


:= C_c2 20.318=

f_cb 30.2MPa:=


C_r 1118 kN= > C_f_LC1 30 kN=

LC1: C_f_LC1C_r

M_f_X_LC1M_r_X

+ 82.358 %= < 100 %


k_se 0.8:= P_epi


12

1.0 l_Beam sys_c2( )22.458 103 kN=:=

LC1: C_f_LC1C_r

2 M_f_X_LC1M_r_X

1

1C_f_LC1

P_e

+ 80.732 %= < 100 %


Page 10 of 103/25/2015

Bracing F_brace_LC1 131kN:=

"Handcalculation" to verify data from internet pages dia_rod 32mm:= a_pitch 3.6mm:= l_emb 31.75mm:=

existing tensile stress area A_t pi4

dia_rod 0.9382 a_pitch( )2:= A_t 643.435 mm2=

maximum tensile strength F_02 A_t 300 MPa:= F_02 193.03 kN=

threaded shear area A_spi

2dia_rod 0.649 a_pitch( ) l_emb:= A_s 1479 mm2=

shear strength thread F_ A_s 0.58 300 MPa:= F_ 257.417 kN=

embedded length req'dl_e

2 A_t350MPa300MPa

0.5 pi dia_rod 0.6495 a_pitch( ):= l_e 32.223 mm=

l_e_Clevins 1 14

in 31.75 mm=:=

dimension "N" as per Cleveland City Forge

Clevis by ClevelandClevis #3 max working load = 15000lbs chosen

T_r 15000lbf1.25 1.5+

2

53

:= max working load has been established with a safety factor of 1: 5(typical for overhead cranes), to bring safety down to normal buildingstandards mulitply with 5/3

T_r 152.908 kN= > F_brace_LC1 131 kN=

mathcad - foss equestrian stables - andre.pdf

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