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 Page 1


Short Notes on Design of Steel Structures 
 
Tension Member 
? A  tension  member  in  which  reversal  of  direct  stress  due  to  loads  other  then  wind  or 
earthquake forces has maximum slenderness ratio =180 
? A member normally acting as a tie in roof truss or bracing system. But subjected to possible 
reversal of stress resulting from the action of wind or earthquake  forces  has  maximum 
slenderness ratio =350 
 
Net Sectional Area 
? For plate: Net area = (b x t) – nd't 
22
12
12
44
ss
t
gg
??
??
??
??
  
 
? Single angle connected by one leg only. 
o 
12 net
AAkA ??
  
 
where, A
1
 = Net cross-section of area of the connected leg. 
A
2
 = Gross cross-sectional area of unconnected leg. (out stand) 
 
o 
1
12
3
3
A
k
A A
?
?
          
o  
11
2
t
At t
??
??
??
??
 
o 
22
2
t
At t
??
??
??
??
       
o 
12
()
net
A II tt ?? ?  
 
? For pair of angle placed back to back (or a signal tee) connected by only one leg of each angle 
(or by the flange of a tee) to the same side of a gusset plate: or it the two angles are tagged 
along a-a. 
Page 2


Short Notes on Design of Steel Structures 
 
Tension Member 
? A  tension  member  in  which  reversal  of  direct  stress  due  to  loads  other  then  wind  or 
earthquake forces has maximum slenderness ratio =180 
? A member normally acting as a tie in roof truss or bracing system. But subjected to possible 
reversal of stress resulting from the action of wind or earthquake  forces  has  maximum 
slenderness ratio =350 
 
Net Sectional Area 
? For plate: Net area = (b x t) – nd't 
22
12
12
44
ss
t
gg
??
??
??
??
  
 
? Single angle connected by one leg only. 
o 
12 net
AAkA ??
  
 
where, A
1
 = Net cross-section of area of the connected leg. 
A
2
 = Gross cross-sectional area of unconnected leg. (out stand) 
 
o 
1
12
3
3
A
k
A A
?
?
          
o  
11
2
t
At t
??
??
??
??
 
o 
22
2
t
At t
??
??
??
??
       
o 
12
()
net
A II tt ?? ?  
 
? For pair of angle placed back to back (or a signal tee) connected by only one leg of each angle 
(or by the flange of a tee) to the same side of a gusset plate: or it the two angles are tagged 
along a-a. 
 
o 
12 net
A AkA ??
 
o  
1
12
5
5
A
k
AA
?
?
  
 where, A
1
 = Area of connected leg 
 A
2
 = Area of outstand (unconnected leg) 
? If two angles are places back to back and connected to both sides of the gusset plate. Then 
 
o 
12
(1)
net
AAAk ?? ?
 
when tack riveted. 
If not tack riveted then both will be considered separately and case (ii) will be followed 
1
12
3
3
A
k
AA
?
?
 
 
Permissible Stress in Design 
? The direct stress in axial tension on the effective net area should not exceeded s
at
 
  where      
?
 s
at
 = 0.5f
y 
? f
y
 = minimum yield stress of steel in MPa 
 
Lug Angle 
? The lug angle is a short length of an angle section used at a joint to connect the outstanding 
leg of a member, thereby reducing the length of the joint. When lug angle is used k = 1 
 
Compression Member 
 
Strength of an Axially Loaded Compression Member 
? The maximum axial compressive load P 
P = s
ac
 x A 
where, 
o P = axial compressive load (n) 
o s
ac
 = permissible stress in axial compression (MPa) 
o A = gross-sectional area of the member (mm
2
) 
o s
ac
 is given as 
1/
0.6
[]
cc y
nn ac n
cc y
ff
ff
?
?
??
?
 
o f
cc
 = elastic critical stress in compression 
2
2
E ?
?
?
?  
Page 3


Short Notes on Design of Steel Structures 
 
Tension Member 
? A  tension  member  in  which  reversal  of  direct  stress  due  to  loads  other  then  wind  or 
earthquake forces has maximum slenderness ratio =180 
? A member normally acting as a tie in roof truss or bracing system. But subjected to possible 
reversal of stress resulting from the action of wind or earthquake  forces  has  maximum 
slenderness ratio =350 
 
Net Sectional Area 
? For plate: Net area = (b x t) – nd't 
22
12
12
44
ss
t
gg
??
??
??
??
  
 
? Single angle connected by one leg only. 
o 
12 net
AAkA ??
  
 
where, A
1
 = Net cross-section of area of the connected leg. 
A
2
 = Gross cross-sectional area of unconnected leg. (out stand) 
 
o 
1
12
3
3
A
k
A A
?
?
          
o  
11
2
t
At t
??
??
??
??
 
o 
22
2
t
At t
??
??
??
??
       
o 
12
()
net
A II tt ?? ?  
 
? For pair of angle placed back to back (or a signal tee) connected by only one leg of each angle 
(or by the flange of a tee) to the same side of a gusset plate: or it the two angles are tagged 
along a-a. 
 
o 
12 net
A AkA ??
 
o  
1
12
5
5
A
k
AA
?
?
  
 where, A
1
 = Area of connected leg 
 A
2
 = Area of outstand (unconnected leg) 
? If two angles are places back to back and connected to both sides of the gusset plate. Then 
 
o 
12
(1)
net
AAAk ?? ?
 
when tack riveted. 
If not tack riveted then both will be considered separately and case (ii) will be followed 
1
12
3
3
A
k
AA
?
?
 
 
Permissible Stress in Design 
? The direct stress in axial tension on the effective net area should not exceeded s
at
 
  where      
?
 s
at
 = 0.5f
y 
? f
y
 = minimum yield stress of steel in MPa 
 
Lug Angle 
? The lug angle is a short length of an angle section used at a joint to connect the outstanding 
leg of a member, thereby reducing the length of the joint. When lug angle is used k = 1 
 
Compression Member 
 
Strength of an Axially Loaded Compression Member 
? The maximum axial compressive load P 
P = s
ac
 x A 
where, 
o P = axial compressive load (n) 
o s
ac
 = permissible stress in axial compression (MPa) 
o A = gross-sectional area of the member (mm
2
) 
o s
ac
 is given as 
1/
0.6
[]
cc y
nn ac n
cc y
ff
ff
?
?
??
?
 
o f
cc
 = elastic critical stress in compression 
2
2
E ?
?
?
?  
o   ? = slenderness ratio = 
I
r
  
 
Maximum Slenderness Ratio  
 
? A member carrying compressive loads resulting from dead load and superimposed loads has 
maximum slenderness ratio = 180 
? A member subjected to compressive loads resulting from wind/earthquake forces provided 
the deformation of such members does not adversely affect the stress in any part of the 
structure= 250 
? A member normally carrying tension but subjected to reversal of stress due to wind or 
earthquake forces=350 
 
 
Sl. No.  Degree  of  end  restraint  of 
compression member 
Recommended  value  of 
effective Length 
Symbol 
1.  Effectively held in  position and 
restrained  against  rotation  at 
both ends 
0.65 L 
 
2.  Effectively  held  in  position  at 
both  ends  restrained  against 
rotation at one end 
0.80 L 
 
3.  Effectively  held  in  position  at 
both  ends,  but  not  restrained 
against rotation  
1.00 L 
 
4.    Effectively held in  position and 
restrained  against  rotation  at 
one  end,  and  at  the  other  end 
restrained  against  rotation  but 
not held in position. 
1.20 L 
 
5.  Effectively held in  position and 
restrained  against  rotation  at 
one  end,  and  at  the  other  end 
partially  restrained  against 
rotation  
1.50 L 
 
Page 4


Short Notes on Design of Steel Structures 
 
Tension Member 
? A  tension  member  in  which  reversal  of  direct  stress  due  to  loads  other  then  wind  or 
earthquake forces has maximum slenderness ratio =180 
? A member normally acting as a tie in roof truss or bracing system. But subjected to possible 
reversal of stress resulting from the action of wind or earthquake  forces  has  maximum 
slenderness ratio =350 
 
Net Sectional Area 
? For plate: Net area = (b x t) – nd't 
22
12
12
44
ss
t
gg
??
??
??
??
  
 
? Single angle connected by one leg only. 
o 
12 net
AAkA ??
  
 
where, A
1
 = Net cross-section of area of the connected leg. 
A
2
 = Gross cross-sectional area of unconnected leg. (out stand) 
 
o 
1
12
3
3
A
k
A A
?
?
          
o  
11
2
t
At t
??
??
??
??
 
o 
22
2
t
At t
??
??
??
??
       
o 
12
()
net
A II tt ?? ?  
 
? For pair of angle placed back to back (or a signal tee) connected by only one leg of each angle 
(or by the flange of a tee) to the same side of a gusset plate: or it the two angles are tagged 
along a-a. 
 
o 
12 net
A AkA ??
 
o  
1
12
5
5
A
k
AA
?
?
  
 where, A
1
 = Area of connected leg 
 A
2
 = Area of outstand (unconnected leg) 
? If two angles are places back to back and connected to both sides of the gusset plate. Then 
 
o 
12
(1)
net
AAAk ?? ?
 
when tack riveted. 
If not tack riveted then both will be considered separately and case (ii) will be followed 
1
12
3
3
A
k
AA
?
?
 
 
Permissible Stress in Design 
? The direct stress in axial tension on the effective net area should not exceeded s
at
 
  where      
?
 s
at
 = 0.5f
y 
? f
y
 = minimum yield stress of steel in MPa 
 
Lug Angle 
? The lug angle is a short length of an angle section used at a joint to connect the outstanding 
leg of a member, thereby reducing the length of the joint. When lug angle is used k = 1 
 
Compression Member 
 
Strength of an Axially Loaded Compression Member 
? The maximum axial compressive load P 
P = s
ac
 x A 
where, 
o P = axial compressive load (n) 
o s
ac
 = permissible stress in axial compression (MPa) 
o A = gross-sectional area of the member (mm
2
) 
o s
ac
 is given as 
1/
0.6
[]
cc y
nn ac n
cc y
ff
ff
?
?
??
?
 
o f
cc
 = elastic critical stress in compression 
2
2
E ?
?
?
?  
o   ? = slenderness ratio = 
I
r
  
 
Maximum Slenderness Ratio  
 
? A member carrying compressive loads resulting from dead load and superimposed loads has 
maximum slenderness ratio = 180 
? A member subjected to compressive loads resulting from wind/earthquake forces provided 
the deformation of such members does not adversely affect the stress in any part of the 
structure= 250 
? A member normally carrying tension but subjected to reversal of stress due to wind or 
earthquake forces=350 
 
 
Sl. No.  Degree  of  end  restraint  of 
compression member 
Recommended  value  of 
effective Length 
Symbol 
1.  Effectively held in  position and 
restrained  against  rotation  at 
both ends 
0.65 L 
 
2.  Effectively  held  in  position  at 
both  ends  restrained  against 
rotation at one end 
0.80 L 
 
3.  Effectively  held  in  position  at 
both  ends,  but  not  restrained 
against rotation  
1.00 L 
 
4.    Effectively held in  position and 
restrained  against  rotation  at 
one  end,  and  at  the  other  end 
restrained  against  rotation  but 
not held in position. 
1.20 L 
 
5.  Effectively held in  position and 
restrained  against  rotation  at 
one  end,  and  at  the  other  end 
partially  restrained  against 
rotation  
1.50 L 
 
6.  Effectively  held  in  position  at 
one  end  but  not  restrained 
against  rotation,  and  at  the 
other  end  restrained  against 
rotation but not held in position
2.00 L 
 
7.  Effectively held in  position and 
restrained  against  rotation  at 
one end but not held in position 
nor  restrained  against  rotation 
at the other end 
2.00 L 
 
 
 
Built-up Compression Member 
Tacking Rivets 
? The slenderness ratio of each member between the connections should not be greater than 
40 nor greater than 0.6 times the most unfavorable slenderness ratio of the whole strut 
? The diameter of the connecting rivets should not be less than the minimum diameter given 
below. 
 
Thickness of member  Minimum diameter of rivets 
UP to 10 mm 
Over 10 mm to 16 mm 
Over 10 mm 
16 mm 
20 mm 
22 mm 
  
 
Lacings 
 
Type of lacing  Effective length I
e 
Single lacing, riveted at ends  Length between inner and rivets on lacing bar (= I, 
as shown in Fig. 17) 
Double lacing, riveted at ends and 
at intersection 
0.7  times  length  between  inner  end  rivets  on 
lacing bars (= 0.7 x I) 
Welded lacing  0.7 times distance between inner ends of effective 
lengths of welds at ends (0.7 xI) 
 
For local Buckling criteria 
min
sec
50
0.7
c
whole tion
L
r
?
?
?
 
Page 5


Short Notes on Design of Steel Structures 
 
Tension Member 
? A  tension  member  in  which  reversal  of  direct  stress  due  to  loads  other  then  wind  or 
earthquake forces has maximum slenderness ratio =180 
? A member normally acting as a tie in roof truss or bracing system. But subjected to possible 
reversal of stress resulting from the action of wind or earthquake  forces  has  maximum 
slenderness ratio =350 
 
Net Sectional Area 
? For plate: Net area = (b x t) – nd't 
22
12
12
44
ss
t
gg
??
??
??
??
  
 
? Single angle connected by one leg only. 
o 
12 net
AAkA ??
  
 
where, A
1
 = Net cross-section of area of the connected leg. 
A
2
 = Gross cross-sectional area of unconnected leg. (out stand) 
 
o 
1
12
3
3
A
k
A A
?
?
          
o  
11
2
t
At t
??
??
??
??
 
o 
22
2
t
At t
??
??
??
??
       
o 
12
()
net
A II tt ?? ?  
 
? For pair of angle placed back to back (or a signal tee) connected by only one leg of each angle 
(or by the flange of a tee) to the same side of a gusset plate: or it the two angles are tagged 
along a-a. 
 
o 
12 net
A AkA ??
 
o  
1
12
5
5
A
k
AA
?
?
  
 where, A
1
 = Area of connected leg 
 A
2
 = Area of outstand (unconnected leg) 
? If two angles are places back to back and connected to both sides of the gusset plate. Then 
 
o 
12
(1)
net
AAAk ?? ?
 
when tack riveted. 
If not tack riveted then both will be considered separately and case (ii) will be followed 
1
12
3
3
A
k
AA
?
?
 
 
Permissible Stress in Design 
? The direct stress in axial tension on the effective net area should not exceeded s
at
 
  where      
?
 s
at
 = 0.5f
y 
? f
y
 = minimum yield stress of steel in MPa 
 
Lug Angle 
? The lug angle is a short length of an angle section used at a joint to connect the outstanding 
leg of a member, thereby reducing the length of the joint. When lug angle is used k = 1 
 
Compression Member 
 
Strength of an Axially Loaded Compression Member 
? The maximum axial compressive load P 
P = s
ac
 x A 
where, 
o P = axial compressive load (n) 
o s
ac
 = permissible stress in axial compression (MPa) 
o A = gross-sectional area of the member (mm
2
) 
o s
ac
 is given as 
1/
0.6
[]
cc y
nn ac n
cc y
ff
ff
?
?
??
?
 
o f
cc
 = elastic critical stress in compression 
2
2
E ?
?
?
?  
o   ? = slenderness ratio = 
I
r
  
 
Maximum Slenderness Ratio  
 
? A member carrying compressive loads resulting from dead load and superimposed loads has 
maximum slenderness ratio = 180 
? A member subjected to compressive loads resulting from wind/earthquake forces provided 
the deformation of such members does not adversely affect the stress in any part of the 
structure= 250 
? A member normally carrying tension but subjected to reversal of stress due to wind or 
earthquake forces=350 
 
 
Sl. No.  Degree  of  end  restraint  of 
compression member 
Recommended  value  of 
effective Length 
Symbol 
1.  Effectively held in  position and 
restrained  against  rotation  at 
both ends 
0.65 L 
 
2.  Effectively  held  in  position  at 
both  ends  restrained  against 
rotation at one end 
0.80 L 
 
3.  Effectively  held  in  position  at 
both  ends,  but  not  restrained 
against rotation  
1.00 L 
 
4.    Effectively held in  position and 
restrained  against  rotation  at 
one  end,  and  at  the  other  end 
restrained  against  rotation  but 
not held in position. 
1.20 L 
 
5.  Effectively held in  position and 
restrained  against  rotation  at 
one  end,  and  at  the  other  end 
partially  restrained  against 
rotation  
1.50 L 
 
6.  Effectively  held  in  position  at 
one  end  but  not  restrained 
against  rotation,  and  at  the 
other  end  restrained  against 
rotation but not held in position
2.00 L 
 
7.  Effectively held in  position and 
restrained  against  rotation  at 
one end but not held in position 
nor  restrained  against  rotation 
at the other end 
2.00 L 
 
 
 
Built-up Compression Member 
Tacking Rivets 
? The slenderness ratio of each member between the connections should not be greater than 
40 nor greater than 0.6 times the most unfavorable slenderness ratio of the whole strut 
? The diameter of the connecting rivets should not be less than the minimum diameter given 
below. 
 
Thickness of member  Minimum diameter of rivets 
UP to 10 mm 
Over 10 mm to 16 mm 
Over 10 mm 
16 mm 
20 mm 
22 mm 
  
 
Lacings 
 
Type of lacing  Effective length I
e 
Single lacing, riveted at ends  Length between inner and rivets on lacing bar (= I, 
as shown in Fig. 17) 
Double lacing, riveted at ends and 
at intersection 
0.7  times  length  between  inner  end  rivets  on 
lacing bars (= 0.7 x I) 
Welded lacing  0.7 times distance between inner ends of effective 
lengths of welds at ends (0.7 xI) 
 
For local Buckling criteria 
min
sec
50
0.7
c
whole tion
L
r
?
?
?
 
Where,  
? L = distance between the centres of connections of the lattice bars to each component  
? 
min
c
r = minimum radius of gyration of the components of compression member 
 
? For a single lacing system on two parallel faces, the force (compressive or tensile) in each bar, 
2sin
V
F
?
?   
? For double lacing system on two parallel planes, the force (compressive or tensile) in each bar, 
4sin
V
F
?
?  
? If the flat lacing bars of width b and thickness t have rivets of diameter d then, 
? Compressive stress in each bar 
force
gross area
ac
F
bt
? ???
?
  
? Tensile stress in each bar
force
net area ( )
at
F
bd t
? ?? ?
??
 
? Numbers of rivets required 
2Fcos
Rivet value
?  
 
Welded connections 
? Lap joint: Overlap  (14) ?  times thickness of bar or member, whichever is less. 
? Butt joints: Full penetration butt weld of fillet weld on each side. Lacing bar should be placed 
opposite to flange or stiffening member of main member. 
  
Slab Base 
? Area of slab base=
axial load in the column
permissible compressive stress in concrete
 
? 
 The thickness of a rectangular slab base as per 
 
2
2
3
4
bs
wb
ta
?
??
??
??
??
 
 
? The thickness of a square slab base plate under a solid round column. 
0
90
10
16 ( )
bs
WB
t
Bd ?
??
?
 
  
 
Structural Fasteners  
Riveting 
 
? Gross dia of rivet or dia of hole 
d' = d + 1.5 mm     for d = 25 mm 
d' = d + 2.0 mm    for d = 25 mm 
where   
 d = Nominal dia of rivet 
d' = Gross dia of rivet or dia of hole… 
? Unwins formula

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FAQs on Steel Structures Formulas for Civil Engineering Exam - Design of Steel Structures - Civil Engineering (CE)

1. What are the common formulas used in steel structures for a civil engineering exam?

Ans. Some common formulas used in steel structures for a civil engineering exam include: - Euler's formula for buckling: Pcr = (π^2 * E * I) / (KL)^2 - Yield strength formula: σy = Fy / A - Ultimate strength formula: σu = Fu / A - Moment of inertia formula: I = (b * h^3) / 12 - Deflection formula: δ = (5 * w * L^4) / (384 * E * I)

2. How is Euler's formula for buckling used in steel structures?

Ans. Euler's formula for buckling is used to determine the critical buckling load that a steel structure can withstand. It takes into account the modulus of elasticity (E), moment of inertia (I), effective length (L), and the slenderness ratio (KL). By calculating the critical buckling load using this formula, engineers can determine the stability and safety of a steel structure under compressive loads.

3. What is the significance of the yield strength formula in steel structures?

Ans. The yield strength formula is significant in steel structures as it helps determine the maximum amount of stress a material can withstand before it starts to deform plastically. By calculating the yield strength using this formula, engineers can ensure that the steel structure is designed to withstand the expected loads without undergoing permanent deformation.

4. How can the moment of inertia formula be used in steel structure design?

Ans. The moment of inertia formula is used to determine the resistance of a steel structure to bending moments. It takes into account the base (b) and height (h) of a structural member and provides a measure of its stiffness. By calculating the moment of inertia, engineers can design steel structures that can withstand the expected bending moments without excessive deflection or failure.

5. Why is the deflection formula important in steel structure analysis?

Ans. The deflection formula is important in steel structure analysis as it helps determine the amount of vertical displacement or bending that a structural member will experience under a given load. By calculating the deflection using this formula, engineers can assess the structural integrity and overall performance of a steel structure, ensuring that it meets the required design criteria and safety standards.

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