Compression Members

Compression Member

Strength of an Axially Loaded Compression Member

The maximum axial compressive load P

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

σ_ac = permissible stress in axial compression (MPa)

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

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

Where, f_cc = elastic critical stress in compression

λ = slenderness ratio =

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 𝛔_acand 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

(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.

Lacings

(a) General requirements:

Radius of gyration about the axis ⊥ to the plane of lacing radius of gyration about the axis in plane of lacing
The lacing system should not be varied throughout the length of the strut as far as practicable.
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 l_e/r of the lacing bars should not exceed 145. The effective length l_e 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.

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:

for single lacing

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,
- For double lacing system on two parallel planes, the force (compressive or tensile) in each bar,
- If the flat lacing bars of width b and thickness t have rivets of diameter d then,
- Compressive stress in each bar
- Tensile stress in each bar

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

For case (b),

Numbers of rivets required
Welded connections
Lap joint: Overlap 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.

Battens

(a) General Requirements:

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

(b) Design Specifications:

Spacing of battens C, from centre to centre of end fastening should be such that the slenderness ratio of the lesser main component, 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.
minimum radius of gyration of components.
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
Thickness of battens,
where, l_b = distance between innermost connecting line of rivets of welds.
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.
  and a moment,
  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,
  where, t_va = 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, σ_bc σ_bt = permissible bending compressive or tensile) stress
  = 165 MPa for steel of IS: 226-1975
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 where t is thickness of plate
- Total length of weld at end of edge of batten
- Length of weld at each edge of batten total length of weld required
- Return weld along transverse axis of column where, t and D are the thickness and overall depth of the battens respectively.

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