Engineering Mechanics & Design of Steel Structures: compression Members

By Ashutosh Yadav|Updated : August 15th, 2021

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Compression Member

Strength of an Axially Loaded Compression Member

  • The maximum axial compressive load P

P = σac x A where, P = axial compressive load (n)

σac = permissible stress in axial compression (MPa)

A = gross-sectional area of the member (mm2)

IS800-1984 uses the Merchant Rankine formula for σac which is given as


Where, fcc = elastic critical stress in compression image018

λ = slenderness ratio = image019

l = effective length of the compression member.

r = appropriate radius of gyration of the member (minimum value)

E = modulus of elasticity of steel = 2 x 105 MPa

n = a factor assumed as 1.4

Maximum Slenderness Ratio (Clause 3.7.1 IS : 800-1984)


Effective Length

Table: (Effective length of compression members of constant dimensions (Clause 5.2.2 IS: 800-1984)


Angle struts

  • The slenderness ratio (λ=I/r) should not exceed the values given in Table.

Table: Angle Struts (Clauses 5.5, IS: 800 – 1984)


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. In no case should the spacing of tacking rivets in a line exceed 600 mm for such members, i.e. two angles, channels or tees placed back-to back.
  • For other types of built-up compression members, say where cover-plates are used, the pitch of tacking rivets should not exceed 32 t or 300 mm, whichever is less, where t is the thickness of the thinner outside plate. When plates are exposed to the weather, the pitch should not exceed 16 t or 200 mm whichever is less.
  • The diameter of the connecting rivets should not be less than the minimum diameter given below.


Design of Compression Members

The following steps are followed for designing an axially loaded compression member:

(i) Assume some value of permissible compressive stress 𝛔ac and calculate the approximate gross sectional area A required


For single-angle-channel-or I-section (low loads) 80 MPa and for built-up sections (heavy loads) 110 MPa may be assumed initially as permissible compressive stress.

(ii) Choose a trial section having area image025

(iii) Determine the actual permissible stress corresponding to maximum slenderness ratio l/r of the trial section.

(iv) Calculate the safe load to be carried by trial section by multiplying, the actual permissible stress by the area of the trial section.

If the safe load is equal to or slightly more than the actual load, the trial section is suitable for selection. Otherwise the above steps should be repeated.

(v) Check the slenderness ratio.


(a) General requirements:

  1. Radius of gyration about the axis ⊥ to the plane of lacing image026 radius of gyration about the axis in plane of lacing
  2. The lacing system should not be varied throughout the length of the strut as far as practicable.
  3. The single-laced system on opposite sides of the main components should preferably be in the same direction so that one be the shadow of the other.

(b) Design Specification:


  • The angle of inclination of the lacing with the longitudinal axis of the column should be between 40° to 70°.
  • The slenderness ratio le/r of the lacing bars should not exceed 145. The effective length le of the lacing bars should be taken as follows:


  • For local Buckling criteria


Where, L = distance between the centres of connections of the lattice bars to each component as shown in fig.

image030 minimum radius of gyration of the components of compression member

  • Minimum width of lacing bars in riveted construction should be as follows:


  • Minimum thickness of lacing bars:

image032 for single lacing

image033 for double lacing riveted or welded at intersection

where, l = length between inner and rivets as shown in fig.

  • The lacing of compression members should be designed to resist a transverse shear, V = 25% of axial force in the member.
    • For a single lacing system on two parallel faces, the force (compressive or tensile) in each bar, image034
    • For double lacing system on two parallel planes, the force (compressive or tensile) in each bar, image035
    • If the flat lacing bars of width b and thickness t have rivets of diameter d then, 
    • Compressive stress in each bar image036
    • Tensile stress in each bar image037


  • End Connections:
    • Riveted Connection: Riveted connections may be made in two ways as shown in Fig. (a) and (b).


For case (a),

Number of rivets required image039

For case (b),

  • Numbers of rivets required image040
  • Welded connections
    Lap joint: Overlap image041 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.


(a) General Requirements:


  • image043
  • The number of battens should be such that the member is divided into not less than three parts longitudinally.

(b) Design Specifications:

  1. Spacing of battens C, from centre to centre of end fastening should be such that the slenderness ratio of the lesser main component, image044 times the slenderness ratio of the compression member as a whole about x – y axis (parallel to battens), which is less
    where C = spacing of battens as shown in fig.
    image001 minimum radius of gyration of components.
  2. image045 for intermediate battens,
    d > a for end battens
    and d > 2 × b for any batten.
    where d = effective depth of batten,
    a = centroid distance of members,
    b = width of member in the plane of batten
  3. Thickness of battens,
    image046 where, lb = distance between innermost connecting line of rivets of welds.
  4. image047 and P = total axial load on the comp. member.
    • Transverse shear V is divided equally between the parallel planes of battens. Battens and their connections to main components resist simultaneously a longitudinal shear.
      image048 and a moment, image049
      where, C = spacing of battens
      N = number of parallel planes of battens
      S = minimum transverse distance between centroids of rivet group or welding.
    • Check for longitudinal shear stress,
      image050 where, tva = permissible average shear stress
      = 100 MPa for steel of IS : 226-1975
      D = overall depth of battens,
      t = thickness of battens.
    • Check for bending stress,
      where, σbc σbt = permissible bending compressive or tensile) stress
      = 165 MPa for steel of IS: 226-1975
  5. End connections:
    • Design the end connections to resist the longitudinal shear force V1 and the moment M as calculated in steep 4 above.
    • For welded connections Lap image052 where t is thickness of plate
    • Total length of weld at end of edge of batten image053
    • Length of weld at each edge of batten image054 total length of weld required
    • Return weld along transverse axis of column image055 where, t and D are the thickness and overall depth of the battens respectively.


image057 t = thickness of batten

Slab Base

  • Sufficient fastenings are provided to retain the column securely on the base plate and resist all moments and forces (except direct compression in the column.) arising during transit, unloading and erection.
  • Area of slab base 


  • The thickness of a rectangular slab base as per IS 800: 1984.



where t = the slab thickness (mm)

w = the pressure or loading on the underside of the base (MPa)

a = the greater projection of the plate beyond the column (mm) = max. (∝, β).

b = the lesser projection of the plate beyond the column (mm) = max. (∝, β).

σbs = the permissible bending stress in slab bases

= 165 MPa for flanged beams

= MPa for solid beams

  • The thickness of a square slab base plate under a solid round column.



W = the total axial load (kN)

B = the length of the side of cap or base (mm)

d0 = the diameter of the reduced end (if any) of the column (mm).

The cap or base plate should not be less 1.5 (d0 +75) mm in length.


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