Verified by the CalcTree engineering team on July 20, 2024 This calculator designs a standard steel section by computing the flexural and axial design capacities to Ultimate Limit State (ULS) methods.
All calculations are performed in accordance with AS4100-2020 .
📃 List of symbols used on this page
A g = g r o s s a r e a o f a c r o s s − s e c t i o n A a = n e t a r e a o f a c r o s s − s e c t i o n A o = p l a i n s h a n k a r e a o f a b o l t A s = t e n s i l e s t r e s s a r e a o f a b o l t ; o r = a r e a o f a s t i f f e n e r o r s t i f f e n e r s i n c o n t a c t w i t h a f l a n g e A w = g r o s s s e c t i o n a l a r e a o f a w e b a e = m i n i m u m d i s t a n c e f r o m t h e e d g e o f a h o l e t o t h e e d g e o f a p l y m e a s u r e d i n t h e d i r e c t i o n o f t h e c o m p o n e n t o f a f o r c e p l u s h a l f t h e b o l t d i a m e t e r . d = d e p t h o f a s e c t i o n d e = e f f e c t i v e o u t s i d e d i a m e t e r o f a c i r c u l a r h o l l o w s e c t i o n d f = d i a m e t e r o f a f a s t e n e r ( b o l t o r p i n ) ; o r = d i s t a n c e b e t w e e n f l a n g e c e n t r o i d s d p = c l e a r t r a n s v e r s e d i m e n s i o n o f a w e b p a n e l ; o r = d e p t h o f d e e p e s t w e b p a n e l i n a l e n g t h d 1 = c l e a r d e p t h b e t w e e n f l a n g e s i g n o r i n g f i l l e t s o r w e l d s d 2 = ‘ t w i c e t h e c l e a r d i s t a n c e f r o m t h e n e u t r a l a x e s t o t h e c o m p r e s s i o n f l a n g e . W = Y o u n g ’ s m o d u l u s o f e l a s t i c i t y , 200 x 10 ° M P a . e = e c c e n t r i c i t y F = a c t i o n i n g e n e r a l , f o r c e o r l o a d f u = t e n s i l e s t r e n g t h u s e d i n d e s i g n f u f = m i n i m u m t e n s i l e s t r e n g t h o f a b o l t f u p = t e n s i l e s t r e n g t h o f a p l y f u w = n o m i n a l t e n s i l e s t r e n g t h o f w e l d m e t a l f y = y i e l d s t r e s s u s e d i n d e s i g n f y s = y i e l d s t r e s s o f a s t i f f e n e r u s e d i n d e s i g n G = s h e a r m o d u l u s o f e l a s t i c i t y , 80 x 10 ° M P a ; o r = n o m i n a l d e a d l o a d I = s e c o n d m o m e n t o f a r e a o f a c r o s s − s e c t i o n I e y = s e c o n d m o m e n t o f a r e a o f c o m p r e s s i o n f l a n g e a b o u t t h e s e c t i o n m i n o r p r i n c i p a l y − a x i s I x = I a b o u t t h e c r o s s − s e c t i o n m a j o r p r i n c i p a l x − a x i s I y = I a b o u t t h e c r o s s − s e c t i o n m i n o r p r i n c i p a l y − a x i s J = t o r s i o n c o n s t a n t f o r a c r o s s − s e c t i k e = m e m b e r e f f e c t i v e l e n g t h f a c t o r k f = f o r m f a c t o r f o r m e m b e r s s u b j e c t t o a x i a l c o m p r e s s i o n k l = l o a d h e i g h t e f f e c t i v e l e n g t h f a c t o r k r = e f f e c t i v e l e n g t h f a c t o r f o r r e s t r a i n t a g a i n s t l a t e r a l r o t a t i o n l = s p a n ; o r , = m e m b e r l e n g t h ; o r , = s e g m e n t o r s u b − s e g m e n t l e n g t h l e / r = g e o m e t r i c a l s l e n d e r n e s s r a t i o l j = l e n g t h o f a b o l t e d l a p s p l i c e c o n n e c t i o n M b = n o m i n a l m e m b e r m o m e n t c a p a c i t y M b x = M b a b o u t m a j o r p r i n c i p a l x − a x i s M c x = l e s s e r o f M i x a n d M o x M o = r e f e r e n c e e l a s t i c b u c k l i n g m o m e n t f o r a m e m b e r s u b j e c t t o b e n d i n g M o o = r e f e r e n c e e l a s t i c b u c k l i n g m o m e n t o b t a i n e d u s i n g / . = M o s = M o b f o r a s e g m e n t , f u l l y r e s t r a i n e d a t b o t h e n d s , u n r e s t r a i n e d a g a i n s t l a t e r a l r o t a t i o n a n d l o a d e d a t s h e a r c e n t r e M o x = n o m i n a l o u t − o f − p l a n e m e m b e r m o m e n t c a p a c i t y a b o u t m a j o r p r i n c i p a l x − a x i s M p r = n o m i n a l p l a s t i c m o m e n t c a p a c i t y r e d u c e d f o r a x i a l f o r c e M p r x = M p r a b o u t m a j o r p r i n c i p a l x − a x i s M p r y = M p r a b o u t m i n o r p r i n c i p a l y − a x i s M r x = M s a b o u t m a j o r p r i n c i p a l x − a x i s r e d u c e d b y a x i a l f o r c e M r y = M s a b o u t m i n o r p r i n c i p a l y − a x i s r e d u c e d b y a x i a l f o r c e M s = n o m i n a l s e c t i o n m o m e n t c a p a c i t y M s x = M s a b o u t m a j o r p r i n c i p a l x − a x i s M s y = M s a b o u t t h e m i n o r p r i n c i p a l y − a x i s M t x = l e s s e r o f M r x a n d M o x M ∗ = d e s i g n b e n d i n g m o m e n t N c = n o m i n a l m e m b e r c a p a c i t y i n c o m p r e s s i o n \small{A_g \ = \ gross \ area \ of \ a \ cross-section } \newline \small{A_a \ = \ net \ area \ of \ a \ cross-section } \newline \small{A_o \ = \ plain \ shank \ area \ of \ a \ bolt } \newline \small{A_s \ = \ tensile \ stress \ area \ of \ a \ bolt; \ or } \newline \small{ \ = \ area \ of \ a \ stiffener \ or \ stiffeners \ in \ contact \ with \ a \ flange } \newline \small{A_w \ = \ gross \ sectional \ area \ of \ a \ web } \newline \small{a_e \ = \ minimum \ distance \ from \ the \ edge \ of \ a \ hole \ to \ the \ edge \ of \ a \ ply \ measured \ in \ the } \newline \small{ direction \ of \ the \ component \ of \ a \ force \ plus \ half \ the \ bolt \ diameter. } \newline \small{d \ = \ depth \ of \ a \ section } \newline \small{d_e \ = \ effective \ outside \ diameter \ of \ a \ circular \ hollow \ section } \newline \small{d_f \ = \ diameter \ of \ a \ fastener \ (bolt \ or \ pin); \ or } \newline \small{ = \ distance \ between \ flange \ centroids } \newline \small{d_p \ = \ clear \ transverse \ dimension \ of \ a \ web \ panel; \ or } \newline \small{ = \ depth \ of \ deepest \ web \ panel \ in \ a \ length } \newline \small{d_1 \ = \ clear \ depth \ between \ flanges \ ignoring \ fillets \ or \ welds } \newline \small{d_2 \ = \ ‘twice \ the \ clear \ distance \ from \ the \ neutral \ axes \ to \ the \ compression \ flange. } \newline \small{W \ = \ Young’s \ modulus \ of \ elasticity, \ 200x10° \ MPa. } \newline \small{e \ = \ eccentricity } \newline \small{F \ = \ action \ in \ general, \ force \ or \ load } \newline \small{f_u \ = \ tensile \ strength \ used \ in \ design } \newline \small{f_{uf} \ = \ minimum \ tensile \ strength \ of \ a \ bolt } \newline \small{f_{up} \ = \ tensile \ strength \ of \ a \ ply } \newline \small{f_{uw} \ = \ nominal \ tensile \ strength \ of \ weld \ metal } \newline \small{f_y \ = \ yield \ stress \ used \ in \ design } \newline \small{f_{ys} \ = \ yield \ stress \ of \ a \ stiffener \ used \ in \ design } \newline \small{G \ = \ shear \ modulus \ of \ elasticity, \ 80x10° \ MPa; \ or } \newline \small{ = \ nominal \ dead \ load } \newline \small{I \ = \ second \ moment \ of \ area \ of \ a \ cross-section } \newline \small{I_{ey} \ = \ second \ moment \ of \ area \ of \ compression \ flange \ about \ the \ section \ minor } \newline \small{ principal \ y- \ axis } \newline \small{I_x \ = \ I \ about \ the \ cross-section \ major \ principal \ x-axis } \newline \small{I_y \ = \ I \ about \ the \ cross-section \ minor \ principal \ y-axis } \newline \small{J \ = \ torsion \ constant \ for \ a \ cross-secti } \newline \small{k_e \ = \ member \ effective \ length \ factor } \newline \small{k_f \ = \ form \ factor \ for \ members \ subject \ to \ axial \ compression } \newline \small{k_l \ = \ load \ height \ effective \ length \ factor } \newline \small{k_r \ = \ effective \ length \ factor \ for \ restraint \ against \ lateral \ rotation } \newline \small{l \ = \ span; \ or, } \newline \small{ = \ member \ length; \ or, } \newline \small{ = \ segment \ or \ sub-segment \ length } \newline \small{l_e/r \ = \ geometrical \ slenderness \ ratio } \newline \small{l_j \ = \ length \ of \ a \ bolted \ lap \ splice \ connection } \newline \small{M_b \ = \ nominal \ member \ moment \ capacity } \newline \small{M_{bx} \ = \ M_b \ about \ major \ principal \ x-axis } \newline \small{M_{cx} \ = \ lesser \ of \ M_{ix} \ and \ M_{ox} } \newline \small{M_o \ = \ reference \ elastic \ buckling \ moment \ for \ a \ member \ subject \ to \ bending } \newline \small{M_{oo} \ = \ reference \ elastic \ buckling \ moment \ obtained \ using \ /. \ = } \newline \small{M_{os} \ = \ M_{ob} \ for \ a \ segment, \ fully \ restrained \ at \ both \ ends, \ unrestrained \ against } \newline \small{ lateral \ rotation \ and \ loaded \ at \ shear \ centre } \newline \small{M_{ox} \ = \ nominal \ out-of-plane \ member \ moment \ capacity \ about \ major \ principal } \newline \small{ x-axis } \newline \small{M_{pr} \ = \ nominal \ plastic \ moment \ capacity \ reduced \ for \ axial \ force } \newline \small{M_{prx} \ = \ M_{pr} \ about \ major \ principal \ x-axis } \newline \small{M_{pry} \ = \ M_{pr} \ about \ minor \ principal \ y-axis } \newline \small{M_{rx} \ = \ M_s \ about \ major \ principal \ x-axis \ reduced \ by \ axial \ force } \newline \small{M_{ry} \ = \ M_s about \ minor \ principal \ y-axis \ reduced \ by \ axial \ force } \newline \small{M_s \ = \ nominal \ section \ moment \ capacity } \newline \small{M_{sx} \ = \ M_s \ about \ major \ principal \ x-axis } \newline \small{M_{sy} \ = \ M_s \ about \ the \ minor \ principal \ y-axis } \newline \small{M_{tx} \ = \ lesser \ of \ M_{rx} \ and \ M_{ox} } \newline \small{M^* \ = \ design \ bending \ moment } \newline \small{N_c \ = \ nominal \ member \ capacity \ in \ compression } \newline A g = g ross a re a o f a cross − sec t i o n A a = n e t a re a o f a cross − sec t i o n A o = pl ain s hank a re a o f a b o lt A s = t e n s i l e s t ress a re a o f a b o lt ; or = a re a o f a s t i ff e n er or s t i ff e n ers in co n t a c t w i t h a f l an g e A w = g ross sec t i o na l a re a o f a w e b a e = minim u m d i s t an ce f ro m t h e e d g e o f a h o l e t o t h e e d g e o f a pl y m e a s u re d in t h e d i rec t i o n o f t h e co m p o n e n t o f a f orce pl u s ha l f t h e b o lt d iam e t er . d = d e pt h o f a sec t i o n d e = e ff ec t i v e o u t s i d e d iam e t er o f a c i rc u l a r h o ll o w sec t i o n d f = d iam e t er o f a f a s t e n er ( b o lt or p in ) ; or = d i s t an ce b e tw ee n f l an g e ce n t ro i d s d p = c l e a r t r an s v erse d im e n s i o n o f a w e b p an e l ; or = d e pt h o f d ee p es t w e b p an e l in a l e n g t h d 1 = c l e a r d e pt h b e tw ee n f l an g es i g n or in g f i ll e t s or w e l d s d 2 = ‘ tw i ce t h e c l e a r d i s t an ce f ro m t h e n e u t r a l a x es t o t h e co m p ress i o n f l an g e . W = Y o u n g ’ s m o d u l u s o f e l a s t i c i t y , 200 x 10° MP a . e = ecce n t r i c i t y F = a c t i o n in g e n er a l , f orce or l o a d f u = t e n s i l e s t re n g t h u se d in d es i g n f u f = minim u m t e n s i l e s t re n g t h o f a b o lt f u p = t e n s i l e s t re n g t h o f a pl y f u w = n o mina l t e n s i l e s t re n g t h o f w e l d m e t a l f y = y i e l d s t ress u se d in d es i g n f ys = y i e l d s t ress o f a s t i ff e n er u se d in d es i g n G = s h e a r m o d u l u s o f e l a s t i c i t y , 80 x 10° MP a ; or = n o mina l d e a d l o a d I = seco n d m o m e n t o f a re a o f a cross − sec t i o n I ey = seco n d m o m e n t o f a re a o f co m p ress i o n f l an g e ab o u t t h e sec t i o n min or p r in c i p a l y − a x i s I x = I ab o u t t h e cross − sec t i o n maj or p r in c i p a l x − a x i s I y = I ab o u t t h e cross − sec t i o n min or p r in c i p a l y − a x i s J = t ors i o n co n s t an t f or a cross − sec t i k e = m e mb er e ff ec t i v e l e n g t h f a c t or k f = f or m f a c t or f or m e mb ers s u bj ec t t o a x ia l co m p ress i o n k l = l o a d h e i g h t e ff ec t i v e l e n g t h f a c t or k r = e ff ec t i v e l e n g t h f a c t or f or res t r ain t a g ain s t l a t er a l ro t a t i o n l = s p an ; or , = m e mb er l e n g t h ; or , = se g m e n t or s u b − se g m e n t l e n g t h l e / r = g eo m e t r i c a l s l e n d er n ess r a t i o l j = l e n g t h o f a b o lt e d l a p s pl i ce co nn ec t i o n M b = n o mina l m e mb er m o m e n t c a p a c i t y M b x = M b ab o u t maj or p r in c i p a l x − a x i s M c x = l esser o f M i x an d M o x M o = re f ere n ce e l a s t i c b u c k l in g m o m e n t f or a m e mb er s u bj ec t t o b e n d in g M oo = re f ere n ce e l a s t i c b u c k l in g m o m e n t o b t ain e d u s in g /. = M os = M o b f or a se g m e n t , f u ll y res t r ain e d a t b o t h e n d s , u n res t r ain e d a g ain s t l a t er a l ro t a t i o n an d l o a d e d a t s h e a r ce n t re M o x = n o mina l o u t − o f − pl an e m e mb er m o m e n t c a p a c i t y ab o u t maj or p r in c i p a l x − a x i s M p r = n o mina l pl a s t i c m o m e n t c a p a c i t y re d u ce d f or a x ia l f orce M p r x = M p r ab o u t maj or p r in c i p a l x − a x i s M p ry = M p r ab o u t min or p r in c i p a l y − a x i s M r x = M s ab o u t maj or p r in c i p a l x − a x i s re d u ce d b y a x ia l f orce M ry = M s ab o u t min or p r in c i p a l y − a x i s re d u ce d b y a x ia l f orce M s = n o mina l sec t i o n m o m e n t c a p a c i t y M s x = M s ab o u t maj or p r in c i p a l x − a x i s M sy = M s ab o u t t h e min or p r in c i p a l y − a x i s M t x = l esser o f M r x an d M o x M ∗ = d es i g n b e n d in g m o m e n t N c = n o mina l m e mb er c a p a c i t y in co m p ress i o n
N c y = N c f o r m e m b e r b u c k i n g a b o u t m i n o r p r i n c i p a l y − a x i s N o m = e l a s t i c f l e x u r a l b u c k l i n g l o a d o f a m e m b e r N o m b = N o m f o r a b r a c e d m e m b e r N o m s = N o m f o r a s w a y m e m b e r N s = n o m i n a l s e c t i o n c a p a c i t y o f a c o m p r e s s i o n m e m b e r ; o r = n o m i n a l s e c t i o n c a p a c i t y f o r a x i a l l o a d N t = n o m i n a l s e c t i o n c a p a c i t y i n t e n s i o n N t f = n o m i n a l t e n s i o n c a p a c i t y o f a b o l t N ∗ = d e s i g n a x i a l f o r c e , t e n s i l e o r c o m p r e s s i v e n e i = n u m b e r o f e f f e c t i v e i n t e r f a c e s Q = n o m i n a l l i v e l o a d R b = n o m i n a l b e a r i n g c a p a c i t y o f a w e b R b b = n o m i n a l b e a r i n g b u c k l i n g c a p a c i t y R b y = n o m i n a l b e a r i n g y i e l d c a p a c i t y R s b = n o m i n a l b u c k l i n g c a p a c i t y o f a s t i f e n e d w e b R s y = n o m i n a l y i e l d c a p a c i t y o f a s t i f f e n e d w e b r = r a d i u s o f g y r a t i o n r y = r a d i u s o f g y r a t i o n a b o u t m i n o r p r i n c i p l e a x i s . S = p l a s t i c s e c t i o n m o d u l u s s = s p a c i n g o f s t i f f e n e r s S g = g a u g e o f b o l t s S p = s t a g g e r e d p i t c h o f b o l t s t = t h i c k n e s s ; o r = t h i c k n e s s o f t h i n n e r p a r t j o i n e d ; o r = w a l l t h i c k n e s s o f c i r c u l a r h o l l o w s e c t i o n ; o r = t h i c k n e s s o f a n a n g l e s e c t i o n t f = t h i c k n e s s o f f l a n g e t p = t h i c k n e s s o f a p l a t e t s = t h i c k n e s s o f a s t i f f e n e r t y = t h i c k n e s s o f a w e b t w , t w 1 , t w 2 , = s i z e o f a f i l l e t w e l d V b = n o m i n a l b e a r i n g c a p a c i t y o f a p l y o r a p i n ; o r = n o m i n a l s h e a r b u c k l i n g c a p a c i t y o f a w e b V f = n o m i n a l s h e a r c a p a c i t y o f a b o l t o r p i n − s t r e n g t h l i m i t s t a t e V s f = n o m i n a l s h e a r c a p a c i t y o f a b o t − s e r v i c e a b i l i t y l i m i t s t a t e V u = n o m i n a l s h e a r c a p a c i t y o f a w e b w i t h a u n i f o r m s h e a r s t r e s s d i s t r i b u t i o n V v = n o m i n a l s h e a r c a p a c i t y o f a w e b V v m = n o m i n a l w e b s h e a r c a p a c i t y i n t h e p r e s e n c e o f b e n d i n g m o m e n t V w = n o m i n a l s h e a r y i e l d c a p a c i t y o f a w e b ; o r = n o m i n a l s h e a r c a p a c i t y o f a p u g o r s l o t w e l d . V ∗ = d e s i g n s h e a r f o r c e V b ∗ = d e s i g n b e a r i n g f o r c e o n a p l y a t a b o l t o r p i n l o c a t o n V f ∗ = d e s i g n s h e a r f o r c e o n a b o l t o r a p i n s t r e n g t h l i m i t s t a t e V w ∗ = d e s i g n s h e a r f o r c e a c t i n g o n a w e b p a n e l y o = ‘ c o o r d i n a t e o f s h e a r c e n t r e Z = e l a s t i c s e c t i o n m o d u l u s Z c = Z e f o r a c o m p a c t s e c t i o n Z e = e f f e c t i v e s e c t i o n m o d u l u s α b = c o m p r e s s i o n m e m b e r s e c t i o n c o n s t a n t α c = c o m p r e s s i o n m e m b e r s l e n d e r n e s s r e d u c t i o n f a c t o r α m = m o m e n t m o d i f i c a t i o n f a c t o r f o r b e n d i n g α s = s l e n d e r n e s s r e d u c t i o n f a c t o r α v = s h e a r b u c k l i n g c o e f f i c i e n t f o r a w e b β e = m o d i f y i n g f a c t o r t o a c c o u n t f o r c o n d i t i o n s a t t h e f a r e n d s o f b e a m = m e m b e r s ξ = c o m p r e s s i o n m e m b e r f a c t o r d e f i n e d i n C l a u s e 6.3.3 o f A S 4100 η = c o m p r e s s i o n m e m b e r i m p e r f e c t i o n f a c t o r d e f i n e d i n C l a u s e 6.3.3 o f A S 4100 λ = s l e n d e r n e s s r a t i o λ e = p l a t e e l e m e n t s l e n d e r e s s λ e d = p l a t e e l e m e n t d e f o r m a t i o n s l e n d e m e s s l i m i t λ e p = p l a t e e l e m e n t p l a s t i c i t y s l e n d e m e s s . λ e y = p l a t e e l e m e n t y i e l d s l e n d e m n e s s l i m i t \small{N_{cy} \ = \ N_c \ for \ member \ bucking \ about \ minor \ principal \ y-axis } \newline \small{N_{om} \ = \ elastic \ flexural \ buckling \ load \ of \ a \ member } \newline \small{N_{omb} \ = \ N_{om} \ for \ a \ braced \ member } \newline \small{N_{oms} \ = \ N_{om} \ for \ a \ sway \ member } \newline \small{N_s \ = \ nominal \ section \ capacity \ of \ a \ compression \ member; \ or } \newline \small{ = \ nominal \ section \ capacity \ for \ axial \ load } \newline \small{N_t \ = \ nominal \ section \ capacity \ in \ tension } \newline \small{N_{tf} \ = \ nominal \ tension \ capacity \ of \ a \ bolt } \newline \small{N^* \ = \ design \ axial \ force, \ tensile \ or \ compressive } \newline \small{n_{ei} \ = \ numberof \ effective \ interfaces } \newline \small{Q \ = \ nominal \ live \ load } \newline \small{R_b \ = \ nominal \ bearing \ capacity \ of \ a \ web } \newline \small{R_{bb} \ = \ nominal \ bearing \ buckling \ capacity } \newline \small{R_{by} \ = \ nominal \ bearing \ yield \ capacity } \newline \small{R_{sb} \ = \ nominal \ buckling \ capacity \ ofa \ stifened \ web } \newline \small{R_{sy} \ = \ nominal \ yield \ capacity \ ofa \ stiffened \ web } \newline \small{r \ = \ radius \ of \ gyration } \newline \small{r_y \ = \ radius \ of \ gyration \ about \ minor \ principle \ axis. } \newline \small{S \ = \ plastic \ section \ modulus } \newline \small{s \ = \ spacing \ of \ stiffeners } \newline \small{S_g \ = \ gauge \ of \ bolts } \newline \small{S_p \ = \ staggered \ pitch \ of \ bolts } \newline \small{t \ = \ thickness; \ or } \newline \small{ = \ thickness \ of \ thinner \ part \ joined; \ or } \newline \small{ = \ wall \ thickness \ of \ circular \ hollow \ section; \ or } \newline \small{ = \ thickness \ of \ an \ angle \ section } \newline \small{t_f \ = \ thickness \ of \ flange } \newline \small{t_p \ = \ thickness \ of \ a \ plate } \newline \small{t_s \ = \ thickness \ of \ a \ stiffener } \newline \small{ty \ = \ thickness \ of \ a \ web } \newline \small{t_w, \ t_{w1}, \ t_{w2}, \ = \ size \ of \ a \ fillet \ weld } \newline \small{V_b \ = \ nominal \ bearing \ capacity \ of \ a \ ply \ or \ a \ pin; \ or } \newline \small{ = \ nominal \ shear \ buckling \ capacity \ of \ a \ web } \newline \small{V_f \ = \ nominal \ shear \ capacity \ ofa \ bolt \ or \ pin \ - \ strength \ limit \ state } \newline \small{V_{sf} \ = \ nominal \ shear \ capacity \ of \ abot \ - \ serviceability \ limit \ state } \newline \small{V_u \ = \ nominal \ shear \ capacity \ of \ a \ web \ with \ a \ uniform \ shear \ stress \ distribution } \newline \small{V_v \ = \ nominal \ shear \ capacity \ ofa \ web } \newline \small{V_{vm} \ = \ nominal \ web \ shear \ capacity \ in \ the \ presence \ of \ bending \ moment } \newline \small{V_w \ = \ nominal \ shear \ yield \ capacity \ of \ a \ web; \ or } \newline \small{ = \ nominal \ shear \ capacity \ of \ a \ pug \ or \ slot \ weld. } \newline \small{V^* \ = \ design \ shear \ force } \newline \small{V^*_b \ = \ design \ bearing \ force \ on \ a \ ply \ at \ a \ bolt \ or \ pin \ locaton } \newline \small{V^*_f \ = \ design \ shear \ force \ on \ a \ bolt \ or \ a \ pin \ ~ \ strength \ limit \ state } \newline \small{V^*_w \ = \ design \ shear \ force \ acting \ on \ a \ web \ panel } \newline \small{y_o \ = \ ‘coordinate \ of \ shear \ centre } \newline \small{Z \ = \ elastic \ section \ modulus } \newline \small{Z_c \ = \ Z_e \ for \ a \ compact \ section } \newline \small{Z_e \ = \ effective \ section \ modulus } \newline \small{\alpha_b\ = \ compression \ member \ section \ constant } \newline \small{\alpha_c\ = \ compression \ member \ slenderness \ reduction \ factor } \newline \small{\alpha_m\ = \ moment \ modification \ factor \ for \ bending } \newline \small{\alpha_s\ = \ slenderness \ reduction \ factor } \newline \small{\alpha_v\ = \ shear \ buckling \ coefficient \ for \ a \ web } \newline \small{\beta_e \ = \ modifying \ factor \ to \ account \ for \ conditions \ at \ the \ far \ ends \ of \ beam } \newline \small{ = \ members } \newline \small{\xi \ = \ compression \ member \ factor \ defined \ in \ Clause \ 6.3.3 \ of \ AS \ 4100 } \newline \small{\eta \ = \ compression \ member \ imperfection \ factor \ defined \ in \ Clause \ 6.3.3 \ of \ AS \ 4100 } \newline \small{\lambda \ = \ slenderness \ ratio } \newline \small{\lambda_e \ = \ plate \ element \ slenderess } \newline \small{\lambda_{ed} \ = \ plate \ element \ deformation \ slendemess \ limit } \newline \small{\lambda_{ep} \ = \ plate \ element \ plasticity \ slendemess. } \newline \small{\lambda_{ey} \ = \ plate \ element \ yield \ slendemness \ limit } \newline N cy = N c f or m e mb er b u c kin g ab o u t min or p r in c i p a l y − a x i s N o m = e l a s t i c f l e xu r a l b u c k l in g l o a d o f a m e mb er N o mb = N o m f or a b r a ce d m e mb er N o m s = N o m f or a s w a y m e mb er N s = n o mina l sec t i o n c a p a c i t y o f a co m p ress i o n m e mb er ; or = n o mina l sec t i o n c a p a c i t y f or a x ia l l o a d N t = n o mina l sec t i o n c a p a c i t y in t e n s i o n N t f = n o mina l t e n s i o n c a p a c i t y o f a b o lt N ∗ = d es i g n a x ia l f orce , t e n s i l e or co m p ress i v e n e i = n u mb ero f e ff ec t i v e in t er f a ces Q = n o mina l l i v e l o a d R b = n o mina l b e a r in g c a p a c i t y o f a w e b R bb = n o mina l b e a r in g b u c k l in g c a p a c i t y R b y = n o mina l b e a r in g y i e l d c a p a c i t y R s b = n o mina l b u c k l in g c a p a c i t y o f a s t i f e n e d w e b R sy = n o mina l y i e l d c a p a c i t y o f a s t i ff e n e d w e b r = r a d i u s o f g yr a t i o n r y = r a d i u s o f g yr a t i o n ab o u t min or p r in c i pl e a x i s . S = pl a s t i c sec t i o n m o d u l u s s = s p a c in g o f s t i ff e n ers S g = g a ug e o f b o lt s S p = s t a gg ere d p i t c h o f b o lt s t = t hi c kn ess ; or = t hi c kn ess o f t hinn er p a r t j o in e d ; or = w a ll t hi c kn ess o f c i rc u l a r h o ll o w sec t i o n ; or = t hi c kn ess o f an an g l e sec t i o n t f = t hi c kn ess o f f l an g e t p = t hi c kn ess o f a pl a t e t s = t hi c kn ess o f a s t i ff e n er t y = t hi c kn ess o f a w e b t w , t w 1 , t w 2 , = s i ze o f a f i ll e t w e l d V b = n o mina l b e a r in g c a p a c i t y o f a pl y or a p in ; or = n o mina l s h e a r b u c k l in g c a p a c i t y o f a w e b V f = n o mina l s h e a r c a p a c i t y o f a b o lt or p in − s t re n g t h l imi t s t a t e V s f = n o mina l s h e a r c a p a c i t y o f ab o t − ser v i ce abi l i t y l imi t s t a t e V u = n o mina l s h e a r c a p a c i t y o f a w e b w i t h a u ni f or m s h e a r s t ress d i s t r ib u t i o n V v = n o mina l s h e a r c a p a c i t y o f a w e b V v m = n o mina l w e b s h e a r c a p a c i t y in t h e p rese n ce o f b e n d in g m o m e n t V w = n o mina l s h e a r y i e l d c a p a c i t y o f a w e b ; or = n o mina l s h e a r c a p a c i t y o f a p ug or s l o t w e l d . V ∗ = d es i g n s h e a r f orce V b ∗ = d es i g n b e a r in g f orce o n a pl y a t a b o lt or p in l oc a t o n V f ∗ = d es i g n s h e a r f orce o n a b o lt or a p in s t re n g t h l imi t s t a t e V w ∗ = d es i g n s h e a r f orce a c t in g o n a w e b p an e l y o = ‘ coor d ina t e o f s h e a r ce n t re Z = e l a s t i c sec t i o n m o d u l u s Z c = Z e f or a co m p a c t sec t i o n Z e = e ff ec t i v e sec t i o n m o d u l u s α b = co m p ress i o n m e mb er sec t i o n co n s t an t α c = co m p ress i o n m e mb er s l e n d er n ess re d u c t i o n f a c t or α m = m o m e n t m o d i f i c a t i o n f a c t or f or b e n d in g α s = s l e n d er n ess re d u c t i o n f a c t or α v = s h e a r b u c k l in g coe ff i c i e n t f or a w e b β e = m o d i f y in g f a c t or t o a cco u n t f or co n d i t i o n s a t t h e f a r e n d s o f b e am = m e mb ers ξ = co m p ress i o n m e mb er f a c t or d e f in e d in Cl a u se 6.3.3 o f A S 4100 η = co m p ress i o n m e mb er im p er f ec t i o n f a c t or d e f in e d in Cl a u se 6.3.3 o f A S 4100 λ = s l e n d er n ess r a t i o λ e = pl a t e e l e m e n t s l e n d eress λ e d = pl a t e e l e m e n t d e f or ma t i o n s l e n d e m ess l imi t λ e p = pl a t e e l e m e n t pl a s t i c i t y s l e n d e m ess . λ ey = pl a t e e l e m e n t y i e l d s l e n d e mn ess l imi t
Calculation Does not account for penetrations or holes, therefore Does not do a shear check or biaxial bending check Input standard steel sections for Universal Beam ( UB ), Universal Column ( UC ), Rectangular Hollow Section ( RHS ), Square Hollow Section ( SHS ), Circular Hollow Section ( CHS ), Equal Angle ( EA ), Unequal Angle ( UA ), Parallel Flange Channel ( PFC ) and Tapered Flange Channel ( TFC ) are as per Liberty Steel 9th Edition catalogue (2019) Input standard sections for Welded Beams ( WB ) and Welded Columns ( WC ) are as per Liberty Steel catalogue 7th Edition catalogue (2014) following AS/NZS 3679.2-400 (as opposed to 300PLUS® welded sections which are produced to exceed the minimum requirements of AS/NZS 3679.2-300). EA is as per x-axis and y-axis (load B) UA is as per n-axis and p-axis PFC is as per x-axis and y-axis (load A) Inputs M*x
: {"mathjs":"Unit","value":20,"unit":"kN m","fixPrefix":false}
V*x
: {"mathjs":"Unit","value":50,"unit":"kN","fixPrefix":false}
V*y
: {"mathjs":"Unit","value":50,"unit":"kN","fixPrefix":false}
👉N* (+) = compression, N* (-) = tension
Capacity checks
N s = k f A n f y Cl 6.2.1 N c = α c N s Cl 6.3.3 N_{s} = k_fA_nf_y \hspace{1cm}\text{Cl 6.2.1}\\N_{c} = \alpha_cN_s\hspace{1cm}\text{Cl 6.3.3} N s = k f A n f y Cl 6.2.1 N c = α c N s Cl 6.3.3
M s = f y Z e Cl 5.2.1 M b = α s α m M s Cl 5.6.1.1 M_{s} = f_y Z_e \hspace{1cm}\text{Cl 5.2.1}\\ M_{b} = \alpha_s \alpha_m M_s \hspace{1cm}\text{Cl 5.6.1.1} M s = f y Z e Cl 5.2.1 M b = α s α m M s Cl 5.6.1.1 👉Note, Mb,x = Mb,y hence a single Mb is reported
Combined Compression and Bending - Section Capacity
M r = M s ( 1 − N ∗ ϕ N s ) Cl 8.3.2 & Cl 8.3.3 \\M_{r}=M_{s}\big(1-\dfrac{N^*}{\phi N_s}\big)\hspace{1cm}\text{Cl 8.3.2 \& Cl 8.3.3} M r = M s ( 1 − ϕ N s N ∗ ) Cl 8.3.2 & Cl 8.3.3
Combined Compression and Bending - In-plane Member Capacity
M i = M s ( 1 − N ∗ ϕ N s ) Cl 8.4.2.2 M_{i}=M_s\big( 1-\dfrac{N^*}{\phi N_{s}}\big)\hspace{1cm}\text{Cl 8.4.2.2} M i = M s ( 1 − ϕ N s N ∗ ) Cl 8.4.2.2
Combined Axial and Bending - Out-of-Plane Member Capacity
M o x = M b x ( 1 − N ∗ ϕ N c y ) Cl 8.4.4.1 M_{ox}=M_{bx}\big(1-\dfrac{N^*}{\phi N_{cy}}\big) \hspace{1cm}\text{Cl 8.4.4.1} M o x = M b x ( 1 − ϕ N cy N ∗ ) Cl 8.4.4.1 Explanation Steel is commonly used to construct building frames, including columns, beams and trusses. These elements provide the necessary structural support for the building. Steel's high strength-to-weight ratio, durability and ductility make it an ideal material for various applications.
Ultimate Limit State (ULS) design for steel includes the following checks against failure phenomena.
Compression Check Section capacity, Ns checks against compressive yielding (squashing) and local buckling.
N s = k f A n f y Cl 6.2.1 N_{s} = k_fA_nf_y\hspace{1cm}\text{Cl 6.2.1} N s = k f A n f y Cl 6.2.1 Only 'stocky' compression members fail by yielding, that is, to have a slenderness ratio l/r < 25 approximately. The form factor is the ratio of the effective to the gross area of the section. If the local buckling form factor, kf = 1.0 then yielding will occur before local buckling, if kf < 1.0 then local buckling will occur before yielding. Member capacity, Nc checks against flexural buckling (or column buckling or Euler buckling).
N c = α c N s Cl 6.3.3 N_{c} = \alpha_cN_s\hspace{1cm}\text{Cl 6.3.3} N c = α c N s Cl 6.3.3 Flexural buckling can only occur in slender compression members, that is, when l/r >= 25 approximately. The theoretical buckling load, Nom, is given by the Euler Equation. The slenderness reduction factor, αc reduces the Euler equation to account for residual stresses and imperfections. Flexural (Euler) Buckling
Flexural Check Section capacity, Ms checks against yielding and local buckling of the compression flange or compression part of web.
M s = f y Z e Cl 5.2.1 M_{s} = f_y Z_e \hspace{1cm}\text{Cl 5.2.1} M s = f y Z e Cl 5.2.1 Effective section modulus, Ze is based on the slenderness classification of a section as either 'slender', 'compact' or 'non-compact'. The classification is used to understand whether the elastic or plastic material limits should be used. Slender sections should use an elastic approach to prevent buckling, whereas a compact section is allowed to develop full plastic capacity. All standard UB and UC sections have been sized such that they not slender. Section behaviour based on slenderness classification
Member capacity, Mb checks against flexural-torsional buckling which is where the beam bends in it's minor axis and twists, as this behaviour is the least stiff bending failure.
M b = α s α m M s Cl 5.6.1.1 \\ M_{b} = \alpha_s \alpha_m M_s\hspace{1cm}\text{Cl 5.6.1.1} M b = α s α m M s Cl 5.6.1.1 The elastic flexural-torsional buckling equation, Mo assumes a perfectly elastic and perfectly straight member with a uniform bending moment. The moment modification factor, αm and the slenderness reduction factor, αs reduces the equation to account for non-uniform bending moment and to account for how restraints impact deformations, respectively. Flexural-torsional buckling won't occur in minor-axis bending as it is already bending in the less stiff axis and it won't occur in CHS or SHS sections since Ix and Iy are equal from symmetry. Flexural-torsional Buckling
Comparison of Steel and Concrete Steel Not inherent, needs intumescent paint
Subject to weather and rust
Related Content Steel Beam and Column Designer to AISC 360 Steel Section Designer to EC3 Check out our library of engineering tools here ! 
