Canopy Solutions L-Bent Canopy Calculator

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AGREE & CONTINUE
Canopy Solutions L-Bent v16
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                         L-Bent / T-Bent Walkway Cover Calculator (ASD)
                      ASCE 7     Version v16      4/13/20
DISCLAIMER: THIS CALCULATOR IS ONLY VALID FOR FLAT ROOF WALKWAY COVERS WITH ZERO SLOPE
Loading
ASCE:
IBC 03/06/09 = ASCE 7-05
IBC 12/15 = ASCE 7-10
IBC 18 = ASCE 7-16
V : mph
V ult : mph
Exposure:
Risk Cat.:
Live Load: psf
Dead Load: psf
Ground Snow Load: psf
Superstructure
Against Host?
MRH:
Mean Roof Height
ft
URL:
Upper Roof Length
ft
PH:
Parapet Height:
ft
Canopy 
Deck Parallel to Walk.?
Post Nearer to Host?
For T-Bents, leave as Yes
W:
Width
ft
S:
Post Spacing
ft
H:
Height to top of post
ft
BS:
Back Span
ft
FS:
Front Span
ft
No. of Gutt./Pur.:
PS1:
Gutter/Purlin spacing 1
ft
PS2:
Gutter/Purlin spacing 2
ft
PS3:
Gutter/Purlin spacing 3
ft
PS4:
Gutter/Purlin spacing 4
ft
Fascia Height:
When decking is perpendicular to walkway, fascia height is net of fascia height AND beam height parallel to walkway
in
Welded Base Plate?
ASD Load Combinations (Post)
Effective Combinations:
Gravity:
Uplift:
1.
2.
3.
4.
5.
6a.
6b.
7.
8.
Legend:
D = Dead Load Lr = Roof Live Load S = Snow Load W = Wind Load
Decking Capacity

INVALID WITHOUT
ENGINEER SEAL
Purlin Capacity

        INVALID WITHOUT ENGINEER SEAL
Beam Capacity

INVALID WITHOUT
ENGINEER SEAL

INVALID WITHOUT
ENGINEER SEAL
Post Capacity

INVALID WITHOUT
ENGINEER SEAL

INVALID WITHOUT
ENGINEER SEAL
Gusset Capacity
Beam:
Post:
Quantity:
Gusset:
in
2" Washer?
1/2" Bolt Capacity:
ASD Reactions to Host Structure at Base of Post
Post:
Gravity:
Uplift:
Moment:
Lateral:
Foundation Design
USCS Soil Class:
GW: Well-graded gravel
GP: Poorly graded gravel
GM: Silty gravel
GC: Clayey gravel
SW: Well-graded sand
SP: Poorly graded sand
SM: Silty sand
SC: Clayey sand
ML: Silt
CL: Lean clay
OL: Organic clay/silt (low plasticity-LL<50)
MH: Elastic silt
CH: Fat clay
OH: Organic clay/silt (high plasticity-LL>=50)
Footing Diameter:
Footing Depth:
Vertical Rebar:
Stirrups:
  Information                                                
  Rain Load (R) is ignored 334461 332450 313492 312330 303631 281991 280718  
  Monoslope, 0 slope, canopies only  
  Load Combo 6a reserved as TX canopy engineers not considering roof maintenance during wind/snow design event  
  Steel decking Fb calculated to replicate manufacturer tested data for bending/deflection  
  Wind direction gamma=90 not considered as worst case tributary on posts occurs a signicant distance away from canopy ends to create average gamma=0,180 coefficients to equal gamma=0 condition  
  Drift snow idealized as UDL as analyzing drift for L-Bents against host with post near/far away from host and T-Bents against host becomes too complex to calculate  
  For post unity, combined bending and axial for lateral wind and vertical D,W,S and separate check for D,Lr axial without lateral wind as roof TX canopy engineers not considering roof maintenance during wind/snow design event  
  Positive sign convention for post moment from wind is clockwise positive  
  D+Lr load combination analyzed as full and partial loading to create (2) worst case scenraios of high bending low axial and low bending high axial  
  Post allow axial and bending stresses increased to matched VA results via factors in OneNote  
  For double posts, moment divided by spacing between posts plus 1" and axial not considered to match results from similar analysis in VA  
  Assuming 15 psf soil adhesion for drained clayey soils for footing uplift calculations, however drained soils can result in 0 psf soil adhesion  
 
  Decking (Moment) Load Combinations   Grav Control Uplift Control   Loads  
  1 D     D      
  2 D     S      
  3     Lr    
  4     Wp    
  5     Wn    
  6a     R 0      
  6b        
  7    
  8 0.6D    
  Max:    
         
  Decking (Deflection) Load Combinations   Grav Control Uplift Control   Loads  
  1 D     D  
  2 D     S  
  3     Lr  
  4     Wp  
  5     Wn  
  6a     R 0  
  6b        
  7    
  8 0.6D    
  Max:    
         
  Beam (Moment) Load Combinations   Grav Control Uplift Control   Loads  
  1 D     D  
  2 D     S  
  3     Lr  
  4     Wp  
  5     Wn  
  6a     R 0  
  6b        
  7    
  8 0.6D    
  Max:    
         
  Beam (Deflection) Load Combinations   Grav Control Uplift Control   Loads  
  1 D     D  
  2 D     S  
  3     Lr  
  4     Wp  
  5     Wn  
  6a     R 0  
  6b        
  7    
  8 0.6D    
  Max:    
         
  Post Load Combinations (D,Lr)   Grav Control Uplift Control   Loads  
  1 D     D  
  2 D     S 0.00  
  3     Lr  
  4     Wp 0.00  
  5     Wn 0.00  
  6a     R 0  
  6b        
  7    
  8 0.6D    
  Max:    
         
  Post Load Combinations (D,W,S) WINDWARD WIND   Grav Control Uplift Control   Loads  
  1 D     D  
  2 D     S  
  3     Lr 0.00  
  4     Wp(CNWa)      
  5     Wn(CNWb)      
  6a     R 0  
  6b        
  7     F(avg) WLp  
  8 0.6D     WLn  
  Max:    
         
  Post Load Combinations (D,W,S) LEEWARD WIND   Grav Control Uplift Control   Loads  
  1 D     D  
  2 D     S  
  3     Lr 0.00  
  4     Wp(CNLa)  
  5     Wn(CNLb)  
  6a     R 0  
  6b        
  7              
  8 0.6D          
  Max:    
         
                                                     
 
  Inputs  
  ASCE  
  V  
  Vult  
  Exposure  
  Risk  
  Live Load 20  
  Dead Load 2  
  Ground Snow  
  Against Host?    
  MRH  
  URL  
  PH  
  Deck Parallel to Walk.?  
  Post Nearer to Host?  
  W  
  S  
  H  
  BS  
  FS  
  No. of Gutters/Purlins  
  PS1  
  PS2  
  PS3  
  PS4  
  Fascia Height  
  Welded Base Plate?  
  Beam (Gusset)  
  Post (Gusset)  
  Quantity  
  Gusset  
  2" Washer?  
  Post (Reactions)  
  USCS Soil Class  
       
  Calculated    
  Deck Span  
  Purlin Trib Width  
  Beam Length  
  R1 (moment,beam)  
  R2 (moment,beam)  
  R3 (moment,beam)  
  R4 (moment,beam)  
  R5 (moment,beam)  
  R1 (def,beam)  
  R2 (def,beam)  
  R3 (def,beam)  
  R4 (def,beam)  
  R5 (def,beam)  
  R1 (mom,post,D+Lr)  
  R2 (mom,post,D+Lr)  
  R3 (mom,post,D+Lr)  
  R4 (mom,post,D+Lr)  
  R5 (mom,post,D+Lr)  
  R1 (mom,post,0,G)  
  R2 (mom,post,0,G)  
  R3 (mom,post,0,G)  
  R4 (mom,post,0,G)  
  R5 (mom,post,0,G)  
  R1 (mom,post,0,U)  
  R2 (mom,post,0,U)  
  R3 (mom,post,0,U)  
  R4 (mom,post,0,U)  
  R5 (mom,post,0,U)  
  R1 (mom,post,180,G)  
  R2 (mom,post,180,G)  
  R3 (mom,post,180,G)  
  R4 (mom,post,180,G)  
  R5 (mom,post,180,G)  
  R1 (mom,post,180,U)  
  R2 (mom,post,180,U)  
  R3 (mom,post,180,U)  
  R4 (mom,post,180,U)  
  R5 (mom,post,180,U)  
  M1 (beam)  
  M2 (beam)  
  M1 (post,D+Lr)  
  M2 (post,D+Lr)  
  def1  
  def2  
  Post Trib Area  
  Fascia Height  
       
                                                     
 
  Decking Capacity  
  Decking   Fb(l) Unity(m) Unity(def)  
  3"x6"x0.065" 6063-T6 Pan          
  3"x6"x0.079" 6063-T6 Pan          
  3"x6"x0.094" 6063-T6 Pan          
  2"x8"x0.065" 6063-T6 Pan          
  2.75"x6"x0.078" 6063-T6 Pan          
  2.75"x6"x0.078" 6063-T6 Cap & Pan        
  4.5"x6"x0.078" 6063-T6 Cap & Pan          
  6"x6"x0.078" 6063-T6 Cap & Pan          
    82.00          
               
  Purlin Capacity                
  Purlin   Fb(l) Unity(m) Unity(def)        
  12"x3.5"x12ga ASTM A653 Gr. 50 Cee Beam 11.00        
       
  Beam Capacity  
  Beam   Fb(l) Unity(m) Unity(def)      
  14.95      
  21.39      
  21.73      
  20.70      
  14.48      
  19.08      
  14.72      
    21.20      
  46.00      
  14.16      
  14.16      
  14.16      
  11.00      
 
  Post Capacity  
  Post   M(req G,0) M(req U,0) M(req L,0) M(req T,0) V(req,0) Unity(m,0) M(req G,180) M(req U,180) M(req L,180) M(req T,180) V(req,180) Unity(m,180) Axial (D,W,S) Unity(co,D,W,S) M(D+Lr,partial) Unity(D+Lr,partial) Axial (D+Lr,par) Unity(co,D+Lr,par) M(D+Lr,full) Unity(D+Lr,full) Axial (D+Lr,full) Unity(co,D+Lr,full) Unity(tot)
   
   
   
   
   
   
   
   
   
   
   
               
   
               
   
 
   
   
   
   
   
 
  Gusset Capacity   M(max) Unity  
  1/2" Bolt Capacity    
 
  Reactions to Host Structure  
  Reaction Type   Gravity (kip) Uplift (kip) Moment (k-ft) Shear (kip)
 
  Post Base        
 
  Foundation Design   HOST  
  Footing Diameter    
  Footing Depth       0   180  
  Vertical Rebar    
  Stirrups   #4 Rebar @ 12" O.C.  
 
DESIGN CRITERIA:     Exposures                          
a z_g z_min
H =  Mean Roof Height
ASCE: 
ASCE 7-05:
IBC 2006
IBC 2009
NCBC 2012
ASCE 7-10:
FBC 2010
IBC 2012
FBC 2014
IBC 2015
1 B 7 1200 30
Θ =  0.0 º Roof Slope
Exposure: 
2 C 9.5 900 15
V =  Wind Velocity (3-Second Gust)
Building Category: 
3 D 11.5 700 7
Vult =  Wind Velocity (3-Second Gust)
Kd =  Directionality Factor
G =  0.85 Gust Effect Factor
Design Live Load: 
ASCE
Kz =  Velocity Pressure Coefficient
Design Dead Load: 
Building Categories
7-05
Kzt =  1 Topographic Factor
1 I 0.77
Building Category:
7-10
I =  Importance Factor
2 II 1
7-16
3 III 1.15
Wind Flow: 
 
4 IV 1.15
L =  Overall Canopy Length
W =  Overall Canopy Width
a = 
Wind Flow
1 Clear
Wind Velocity
2 Obstructed
LOADS ON DECKING:   1                          
L1 =  Effective Deck Panel Length
Effective Wind Area (Deck Fasteners)
Effective Wind Area (Roof Deck)
W1 =  Effective Deck Panel Width (per ASCE 7 Sec. 6.2)
A =  Effective Wind Area, L1*W1
Cn Values (C&C)
Cn Values (C&C)
CNp =  Positive Pressure Coefficient (Zone 3)
Angle Eff. Area Clear+ Clear- Obstruct+ Obstruct-
Angle Eff. Area Clear+ Clear- Obstruct+ Obstruct-
CNn =  Negative Pressure Coefficient (Zone 3)
0 1 2.4 -3.3 1 -3.6
0 1 2.4 -3.3 1 -3.6
qz =  Velocity Pressure
For Deflection Check Only:
0 2 1.8 -1.7 0.8 -1.8
0 2 1.8 -1.7 0.8 -1.8
WLp =  Positive Wind Load, = qz*G*CNp
WLp' =  (0.42*WLp)
0 3 1.2 -1.1 0.5 -1.2
0 3 1.2 -1.1 0.5 -1.2
WLn =  Negative Wind Load, = qz*G*CNn
WLn' =  (0.42*WLn)
1
1
2
2
Grav = 
Grav = 
3
3
Uplift = 
Uplift = 
7.5 1 3.2 -4.2 1.6 -5.1
7.5 1 3.2 -4.2 1.6 -5.1
7.5 2 2.4 -2.1 1.2 -2.6
7.5 2 2.4 -2.1 1.2 -2.6
7.5 3 1.6 -1.4 0.8 -1.7
7.5 3 1.6 -1.4 0.8 -1.7
LOADS ON BEAMS:   1   1
2
2
L1 =  Effective Deck Panel Length
3
3
W1 =  Effective Deck Panel Width
15 1 3.6 -3.8 2.4 -4.2
15 1 3.6 -3.8 2.4 -4.2
A =  Effective Wind Area, L1*W1
15 2 2.7 -2.9 1.8 -3.2
15 2 2.7 -2.9 1.8 -3.2
15 3 1.8 -1.9 1.2 -2.1
15 3 1.8 -1.9 1.2 -2.1
CNp =  Positive Pressure Coefficient (Zone 3)
1
1
CNn =  Negative Pressure Coefficient (Zone 3)
2
2
qz =  Velocity Pressure
For Deflection Check Only:
3
3
WLp =  Positive Wind Load, = qz*G*CNp
WLp' =  (0.42*WLp)
30 1 5.2 -5 3.2 -4.6
30 1 5.2 -5 3.2 -4.6
WLn =  Negative Wind Load, = qz*G*CNn
WLn' =  (0.42*WLn)
30 2 3.9 -3.8 2.4 -3.5
30 2 3.9 -3.8 2.4 -3.5
30 3 2.6 -2.5 1.6 -2.3
30 3 2.6 -2.5 1.6 -2.3
Grav = 
Grav = 
1
1
Uplift = 
Uplift = 
2
2
3
3
45 1 5.2 -4.6 4.2 -3.8
45 1 5.2 -4.6 4.2 -3.8
LOADS ON MAIN WIND FORCE RESISTING SYSTEM:   45 2 3.9 -3.5 3.2 -2.9   45 2 3.9 -3.5 3.2 -2.9
(Anchors, Columns, Foundations)
45 3 2.6 -2.3 2.1 -1.9
45 3 2.6 -2.3 2.1 -1.9
Wind Direction, γ = 0º
Wind Direction, γ = 180º
CNWa =  Cnw value, load case A
CNWa =  Cnw value, load case A
CNWb =  Cnw value, load case B
CNWb =  Cnw value, load case B
CNLa =  Cnl value, load case A
CNLa =  Cnl value, load case A
CNLb =  Cnl value, load case B
CNLb =  Cnl value, load case B
Cn Values (MWFRS)
Angle Load Case Windward Leeward
γ = 90º
Wind Direction, γ = 90º
Clear Obstructed Clear Obstructed
Load Case Clear Obstructed
CNa =  Cn value, load case A
CNb =  Cn value, load case B
CNW CNL CNW CNL CNW CNL CNW CNL
0 A 1.2 0.3 -0.5 -1.2 1.2 0.3 -0.5 -1.2
A -0.8 -1.2
CNp =  Critical Positive Pressure Coefficient
0 B -1.1 -0.1 -1.1 -0.6 -1.1 -0.1 -1.1 -0.6
B 0.8 0.5
CNn =  Critical Negative Pressure Coefficient
7.5 A -0.6 -1 -1 -1.5 0.9 1.5 -0.2 -1.2
7.5 B -1.4 0 -1.7 -0.8 1.6 0.3 0.8 -0.3
WLp =  Critical Positive Wind Load, = qz*G*CNp
WLp = 
A
WLn =  Critical Negative Wind Load, = qz*G*CNn
WLn = 
B
15 A -0.9 -1.3 -1.1 -1.5 1.3 1.6 0.4 -1.1
Grav = 
15 B -1.9 0 -2.1 -0.6 1.8 0.6 1.2 -0.3
Uplift = 
A
B
22.5 A -1.5 -1.6 -1.5 -1.7 1.7 1.8 0.5 -1
LOADS ON CANOPY FASCIA:   22.5 B -2.4 -0.3 -2.3 -0.9 2.2 0.7 1.3 0        
A
GCpn1 =  1.5 Combined Net Pressure Coefficient on windward fascia
B
GCpn1 =  -1 Combined Net Pressure Coefficient on leeward fascia
30 A -1.8 -1.8 -1.5 -1.8 2.1 2.1 0.6 -1
30 B -2.5 -0.5 -2.3 -1.1 2.6 1 1.6 0.1
WLp =  Positive Wind Load on Fascia, qz*GCpn1x0.6
A
WLn =  Negative Wind Load on Fascia, qz*GCpn1x0.6
B
WL =  Average Wind Load on Fascia, qz*GCpn1
37.5 A -1.8 -1.8 -1.5 -1.8 2.1 2.2 0.7 -0.9
37.5 B -2.4 -0.6 -2.2 -1.1 2.7 1.1 1.9 0.3
A
B
45 A -1.6 -1.8 -1.3 -1.8 2.2 2.5 0.8 -0.9
45 B -2.3 -0.7 -1.9 -1.2 2.6 1.4 2.1 0.4
A
B
Hollow Structural Rectangular HSS Tubing Design
Inertia based on round corners r=min(t1,t2) & R=(2)min(t1,t2)
Allowable Stress Design per AISC 360-05 Manual of Steel Construction 13th Ed.
about axis "x" about axis "y"
Material Properties:
Fy = Minimum yield stress, ASTM A500 grade B
b = b 1 = b = b 1 =
Fu = Minimum tension strength
d = d 1 = d = d 1 =
E = Modulus of elasticity
G = 11,200 ksi Shear modulus of elasticity of steel
r = r = r = r =
Member Properties:
c = c = c = c =
b = Beam Flange
J = Torsional constant
A = A = A = A =
t1 = Flange Thickness C = HSS Torsional constant
d = d = d = d =
d = Beam Web
Cw =
For hollow structural sections HSS, warping deformations are small, and the warping torsional constant is generally taken as zero
 0 in^6
Warping constant
PART A
PART A
PART A
PART A
t2 = Web Thickness H = Flexural constant (E4-8)
Ic = Ic = Ic = Ic =
Ix = Moment of Inertia (strong) L = Length of member
A = A = A = A =
Iy = Moment of Inertia (weak) K =
Note All Design Checks for Fixed Bottom, Free top, but FYI:
Both ends fixed: 0.5
Fixed bottom, pinned top translation fixed: 0.7
Fixed bottom, fixed top translation free: 1.0
Pinned both ends, translation fixed: 1.0
Fixed bottom, top free: 2.0
Pinned bottom, fixed top translation free: 2.0
K factor (for use with columns)
d = d = d = d =
Sx = Elastic section modulus (strong) KLx = Strong axis effective length
PART B
PART B
PART B
PART B
Sy = Elastic section modulus (weak) KLy = Weak axis effective length
Ic = Ic = Ic = Ic =
Zx = Plastic section modulus (strong) KLz = Effec. length for torsional buckling
A = A = A = A =
Zy = Plastic section modulus (strong) Lv = Dist. from max. to zero shear force
d = d = d = d =
Ag = Gross area of member Defl =
Per ASCE 7
Deflection Limit
Ae = Effective net area of member
Support
A+B = A+B = A+B = A+B =
rx = Radius of Gyration (strong)
I cx = I cx = I cx = I cx =
ry = Radius of Gyration (weak)
I x =
I x =
ro² = Polar radius of gyration about the shear center (E4-7)
Member Loads:
A g = A g =
Mx = Applied moment
My = Applied moment
Tn = Applied torsion
Vx = Applied shear load
Vy = Applied shear load
V = Applied resultant shear load
P = Applied axial compression load
T = Applied axial tension load
Check Allowable Tension:
Pn = Nominal tensile yielding strenght (D2-1)
Pn = Nominal tensile rupture strenght (D2-2)
ALLOWABLE TENSION: Pn/Wt =
MAX REQUIRED TENSION: Tmax =
Check Allowable Compression:
Check for Limiting Width-Thickness Ratios (Compact/Noncompact):
Flanges
b/t
Section B4: If the corner radius is not known, b and d shall be taken as the outside dimension less three times the design wall thickness. This is generally a conservative assumption.
= (b-3*t2)/t1
1.12√E/Fy = Compact Limit per Table B4.1
1.40√E/Fy = NonCompact Limit per Table B4.1
kL/r =
4.71√E/Fy = Limit state of flexural buckling
Compressive strength for flexural buckling of members without slender elements
Fe = Elastic critical buckling stress (E3-4)
Compressive strength for torsional and flexural-torsional buckling of members without slender elements
Fex = Elastic critical buckling stress (E4-9)
Fey = Elastic critical buckling stress (E4-10)
Fez = Elastic critical buckling stress (E4-11)
Fe = Elastic critical buckling stress (E4-5)
Fe = Elastic critical buckling stress governing
Fcr =
Pn = Nominal compressive strenght (E3-1)
Compressive strength for flexural, torsional and flexural-torsional buckling of members with slender elements
0.56√E/Fy = Inferior Limit (E7-4)
1.03√E/Fy = Superior Limit (E7-6)
Qs =
Fe = Elastic critical buckling stress governing: MIN (E3-4;E4-5)
Fcr =
Pn = Nominal compressive strenght (E7-1)
ALLOWABLE COMPRESSION: Pn/Wc =
MAX REQ'D COMPRESSION: Pmax =
Check Allowable Bending:
Check for Limiting Width-Thickness Ratios (Compact/Noncompact):
Flanges
b/t
Section B4: If the corner radius is not known, b and d shall be taken as the outside dimension less three times the design wall thickness. This is generally a conservative assumption.
= (b-3*t2)/t1
1.12√E/Fy = Compact Limit per Table B4.1
1.40√E/Fy = NonCompact Limit per Table B4.1
Webs
d/t
Section B4: If the corner radius is not known, b and d shall be taken as the outside dimension less three times the design wall thickness. This is generally a conservative assumption.
= (d-3*t1)/t2
2.42√E/Fy = Compact Limit per Table B4.1
5.70√E/Fy = NonCompact Limit per Table B4.1
About Strong Axis 
(1): Yielding Limit State
This criteria applies to all members, compact or noncompact webs and compact, noncompact or slender flanges
Mn=Mp=Fy*Zx= (F7-1)
Mn/Wb =
(2): Flange Local Buckling Limit State
This criteria applies to sections with noncompact flanges
(F7-2)
Mn=
Mn/Wb =
This criteria applies to sections with slender flanges
(F7-4)
b e = Effective width of compression flange
S eff = Effective section modulus determiend with b e                          
Mn=FyS eff = (F7-3)   Mn/Wb =                          
(3): Web Local Buckling Limit State
This criteria applies to sections with noncompact webs
(F7-5)
Mn=
Mn/Wb =
ALLOWABLE MOMENT: Mn/Wb = or
MAX REQUIRED MOMENT: Mmax = or
About Weak Axis 
(1): Yielding Limit State
This criteria applies to all members, compact or noncompact webs and compact, noncompact or slender flanges
Mn=Mp=Fy*Zy= (F7-1)
Mn/Wb =
(2): Flange Local Buckling Limit State
This criteria applies to sections with noncompact flanges
(F7-2)
Mn=
Mn/Wb =
This criteria applies to sections with slender flanges
(F7-4)
b e = Effective width of compression flange
S eff = Effective section modulus determiend with b e                          
Mn=FyS eff = (F7-3)   Mn/Wb =                          
(3): Web Local Buckling Limit State
This criteria applies to sections with noncompact webs
(F7-5)
Mn=
Mn/Wb =
ALLOWABLE MOMENT: Mn/Wb = or
MAX REQUIRED MOMENT: Mmax = or
Check Allowable Torsion:
h/t
Section B4: If the corner radius is not known, b and d shall be taken as the outside dimension less three times the design wall thickness. This is generally a conservative assumption.
= (d-3*t1)/t2 (B4-1b.d)
2.45√E/Fy = Inferior Limit
3.07√E/Fy = Superior Limit
Fcr = Critical stress: Fcr=0.6Fy (H3-3)
(H3-4)
(H3-5)
Tn = Torsional strenght: Tn= (Fcr)(C) (H3-1)
Tn/Wt =
ALLOWABLE TORSION: Tn/Wt = or
MAX REQUIRED TORSION: Tmax = or
Check Allowable Shear:
d/tw
Section B4: If the corner radius is not known, b and d shall be taken as the outside dimension less three times the design wall thickness. This is generally a conservative assumption.
= (d-3*t1)/t2
Kv = 5.0
1.10√KvE/Fy =
1.37√KvE/Fy =
Cv =
Aw =
If the corner radius is not known, d shall be taken as the corresponding outside dimension minus three times the thicknesss
Web area
Vn = Nominal shear strenght (G2-1)
ALLOWABLE SHEAR: Vn/Wc =
MAX REQUIRED SHEAR: Vmax =
Check Combined Bending and Axial Compression:
(H1-1a)
1.0
(H1-1b)
Check Combined Bending and Axial Tension:
(H1-1a)
1.0
(H1-1b)
Check Combined Torsion, Shear, Bending and Axial compression:
1.0 (H3-6)
Check Combined Torsion, Shear, Bending and Axial tension:
1.0 (H3-6)
Check Member Deflection (Strong Axis):
W =  Total Loading on Beam in Strong Direction
ALLOWABLE DEFLECTION: ∆Allow =
Simple
Fixed
MAXIMUM DEFLECTION: ∆Max =
Cantilever
Check Member Deflection (Weak Axis):
W =  Total Loading on Beam in Weak Direction
ALLOWABLE DEFLECTION: ∆Allow =
Simple
Fixed
MAXIMUM DEFLECTION: ∆Max =
Cantilever
Hollow Structural Rectangular HSS Tubing Design
Inertia based on round corners r=min(t1,t2) & R=(2)min(t1,t2)
Allowable Stress Design per AISC 360-05 Manual of Steel Construction 13th Ed.
about axis "x" about axis "y"
Material Properties:
Fy = Minimum yield stress, ASTM A500 grade B
b = b 1 = b = b 1 =
Fu = Minimum tension strength
d = d 1 = d = d 1 =
E = Modulus of elasticity
G = 11,200 ksi Shear modulus of elasticity of steel
r = r = r = r =
Member Properties:
c = c = c = c =
b = Beam Flange
J = Torsional constant
A = A = A = A =
t1 = Flange Thickness C = HSS Torsional constant
d = d = d = d =
d = Beam Web
Cw =
For hollow structural sections HSS, warping deformations are small, and the warping torsional constant is generally taken as zero
 0 in^6
Warping constant
PART A
PART A
PART A
PART A
t2 = Web Thickness H = Flexural constant (E4-8)
Ic = Ic = Ic = Ic =
Ix = Moment of Inertia (strong) L = Length of member
A = A = A = A =
Iy = Moment of Inertia (weak) K =
Note All Design Checks for Fixed Bottom, Free top, but FYI:
Both ends fixed: 0.5
Fixed bottom, pinned top translation fixed: 0.7
Fixed bottom, fixed top translation free: 1.0
Pinned both ends, translation fixed: 1.0
Fixed bottom, top free: 2.0
Pinned bottom, fixed top translation free: 2.0
K factor (for use with columns)
d = d = d = d =
Sx = Elastic section modulus (strong) KLx = Strong axis effective length
PART B
PART B
PART B
PART B
Sy = Elastic section modulus (weak) KLy = Weak axis effective length
Ic = Ic = Ic = Ic =
Zx = Plastic section modulus (strong) KLz = Effec. length for torsional buckling
A = A = A = A =
Zy = Plastic section modulus (strong) Lv = Dist. from max. to zero shear force
d = d = d = d =
Ag = Gross area of member Defl =
Per ASCE 7
Deflection Limit
Ae = Effective net area of member
Support
A+B = A+B = A+B = A+B =
rx = Radius of Gyration (strong)
I cx = I cx = I cx = I cx =
ry = Radius of Gyration (weak)
I x =
I x =
ro² = Polar radius of gyration about the shear center (E4-7)
Member Loads:
A g = A g =
Mx = Applied moment
My = Applied moment
Tn = Applied torsion
Vx = Applied shear load
Vy = Applied shear load
V = Applied resultant shear load
P = Applied axial compression load
T = Applied axial tension load
Check Allowable Tension:
Pn = Nominal tensile yielding strenght (D2-1)
Pn = Nominal tensile rupture strenght (D2-2)
ALLOWABLE TENSION: Pn/Wt =
MAX REQUIRED TENSION: Tmax =
Check Allowable Compression:
Check for Limiting Width-Thickness Ratios (Compact/Noncompact):
Flanges
b/t
Section B4: If the corner radius is not known, b and d shall be taken as the outside dimension less three times the design wall thickness. This is generally a conservative assumption.
= (b-3*t2)/t1
1.12√E/Fy = Compact Limit per Table B4.1
1.40√E/Fy = NonCompact Limit per Table B4.1
kL/r =
4.71√E/Fy = Limit state of flexural buckling
Compressive strength for flexural buckling of members without slender elements
Fe = Elastic critical buckling stress (E3-4)
Compressive strength for torsional and flexural-torsional buckling of members without slender elements
Fex = Elastic critical buckling stress (E4-9)
Fey = Elastic critical buckling stress (E4-10)
Fez = Elastic critical buckling stress (E4-11)
Fe = Elastic critical buckling stress (E4-5)
Fe = Elastic critical buckling stress governing
Fcr =
Pn = Nominal compressive strenght (E3-1)
Compressive strength for flexural, torsional and flexural-torsional buckling of members with slender elements
0.56√E/Fy = Inferior Limit (E7-4)
1.03√E/Fy = Superior Limit (E7-6)
Qs =
Fe = Elastic critical buckling stress governing: MIN (E3-4;E4-5)
Fcr =
Pn = Nominal compressive strenght (E7-1)
ALLOWABLE COMPRESSION: Pn/Wc =
MAX REQ'D COMPRESSION: Pmax =
Check Allowable Bending:
Check for Limiting Width-Thickness Ratios (Compact/Noncompact):
Flanges
b/t
Section B4: If the corner radius is not known, b and d shall be taken as the outside dimension less three times the design wall thickness. This is generally a conservative assumption.
= (b-3*t2)/t1
1.12√E/Fy = Compact Limit per Table B4.1
1.40√E/Fy = NonCompact Limit per Table B4.1
Webs
d/t
Section B4: If the corner radius is not known, b and d shall be taken as the outside dimension less three times the design wall thickness. This is generally a conservative assumption.
= (d-3*t1)/t2
2.42√E/Fy = Compact Limit per Table B4.1
5.70√E/Fy = NonCompact Limit per Table B4.1
About Strong Axis 
(1): Yielding Limit State
This criteria applies to all members, compact or noncompact webs and compact, noncompact or slender flanges
Mn=Mp=Fy*Zx= (F7-1)
Mn/Wb =
(2): Flange Local Buckling Limit State
This criteria applies to sections with noncompact flanges
(F7-2)
Mn=
Mn/Wb =
This criteria applies to sections with slender flanges
(F7-4)
b e = Effective width of compression flange
S eff = Effective section modulus determiend with b e                          
Mn=FyS eff = (F7-3)   Mn/Wb =                          
(3): Web Local Buckling Limit State
This criteria applies to sections with noncompact webs
(F7-5)
Mn=
Mn/Wb =
ALLOWABLE MOMENT: Mn/Wb = or
MAX REQUIRED MOMENT: Mmax = or
About Weak Axis 
(1): Yielding Limit State
This criteria applies to all members, compact or noncompact webs and compact, noncompact or slender flanges
Mn=Mp=Fy*Zy= (F7-1)
Mn/Wb =
(2): Flange Local Buckling Limit State
This criteria applies to sections with noncompact flanges
(F7-2)
Mn=
Mn/Wb =
This criteria applies to sections with slender flanges
(F7-4)
b e = Effective width of compression flange
S eff = Effective section modulus determiend with b e                          
Mn=FyS eff = (F7-3)   Mn/Wb =                          
(3): Web Local Buckling Limit State
This criteria applies to sections with noncompact webs
(F7-5)
Mn=
Mn/Wb =
ALLOWABLE MOMENT: Mn/Wb = or
MAX REQUIRED MOMENT: Mmax = or
Check Allowable Torsion:
h/t
Section B4: If the corner radius is not known, b and d shall be taken as the outside dimension less three times the design wall thickness. This is generally a conservative assumption.
= (d-3*t1)/t2 (B4-1b.d)
2.45√E/Fy = Inferior Limit
3.07√E/Fy = Superior Limit
Fcr = Critical stress: Fcr=0.6Fy (H3-3)
(H3-4)
(H3-5)
Tn = Torsional strenght: Tn= (Fcr)(C) (H3-1)
Tn/Wt =
ALLOWABLE TORSION: Tn/Wt = or
MAX REQUIRED TORSION: Tmax = or
Check Allowable Shear:
d/tw
Section B4: If the corner radius is not known, b and d shall be taken as the outside dimension less three times the design wall thickness. This is generally a conservative assumption.
= (d-3*t1)/t2
Kv = 5.0
1.10√KvE/Fy =
1.37√KvE/Fy =
Cv =
Aw =
If the corner radius is not known, d shall be taken as the corresponding outside dimension minus three times the thicknesss
Web area
Vn = Nominal shear strenght (G2-1)
ALLOWABLE SHEAR: Vn/Wc =
MAX REQUIRED SHEAR: Vmax =
Check Combined Bending and Axial Compression:
(H1-1a)
1.0
(H1-1b)
Check Combined Bending and Axial Tension:
(H1-1a)
1.0
(H1-1b)
Check Combined Torsion, Shear, Bending and Axial compression:
1.0 (H3-6)
Check Combined Torsion, Shear, Bending and Axial tension:
1.0 (H3-6)
Check Member Deflection (Strong Axis):
W =  Total Loading on Beam in Strong Direction
ALLOWABLE DEFLECTION: ∆Allow =
Simple
Fixed
MAXIMUM DEFLECTION: ∆Max =
Cantilever
Check Member Deflection (Weak Axis):
W =  Total Loading on Beam in Weak Direction
ALLOWABLE DEFLECTION: ∆Allow =
Simple
Fixed
MAXIMUM DEFLECTION: ∆Max =
Cantilever
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