The slenderness ratio (as per IS : 800) of a member, carrying compressive loads arising from combined dead loads and imposed loads, should not exceed
180
Understanding Slenderness Ratio in Steel Structures (IS 800)
The slenderness ratio is a crucial parameter in the design of steel compression members. It is defined as the ratio of the effective length of the member to its least radius of gyration. A high slenderness ratio indicates that the member is prone to buckling under compressive loads. Indian Standard (IS) 800, the code of practice for general construction in steel, provides limits on the slenderness ratio for various types of members and loading conditions to ensure structural stability and prevent premature buckling failure.
For compression members, limiting the slenderness ratio is particularly important because they are susceptible to buckling instability, which can occur even at stresses below the yield strength of the steel.
IS 800 Limits for Compression Members under Specific Loads
IS 800 specifies maximum permissible slenderness ratios depending on the function of the member and the nature of the loads it carries. For members subjected to compressive forces, different limits apply based on whether the loads are primarily from dead and imposed loads, or from wind and seismic forces.
The question specifically asks for the maximum slenderness ratio for a member carrying compressive loads arising from combined dead loads and imposed loads. According to IS 800, the maximum slenderness ratio for such a member is limited to prevent instability under typical service loads.
Based on the provisions of IS 800 (specifically Clause 3.7.1 in the 2007 version, which deals with limiting deflections and slenderness ratios), the maximum slenderness ratio for a compression member that carries loads resulting from the combination of dead loads and imposed loads (live loads) should not exceed 180. This limit ensures that the member has sufficient stiffness to resist buckling under these common load combinations.
Analyzing the Given Options
Let's examine the provided options in light of the IS 800 standard for compression members under combined dead and imposed loads:
- Option 1: 180
- Option 2: 250
- Option 3: 350
- Option 4: 380
Comparing these options with the IS 800 limit for the specified loading condition (combined dead and imposed loads on a compression member), we find that the standard limit is 180.
Conclusion: Maximum Permissible Slenderness Ratio
As per IS 800, the slenderness ratio of a member carrying compressive loads arising from combined dead loads and imposed loads must not exceed 180. This limit is set to ensure the stability and safety of the steel structure under gravity loads.
Revision Table: IS 800 Slenderness Ratio Limits
| Member Type | Load Type | Maximum Slenderness Ratio (as per IS 800:2007) |
|---|---|---|
| Member carrying compressive loads | Combined Dead Loads and Imposed Loads | 180 |
| Member carrying compressive loads | Due to Wind or Seismic Forces Only | 250 |
| Member whose buckling does not adversely affect the strength of structure | (e.g., bracings) | 250 |
| Member always in tension | (Except pre-tensioned members) | 400 |
| Compression flange of a beam | Against lateral torsional buckling | 300 |
Additional Information on Slenderness Ratio Calculations
The slenderness ratio ($\lambda$) of a member is a non-dimensional quantity calculated using the formula:
\(\lambda = \frac{L_{eff}}{r_{min}}\)
- \(L_{eff}\) (Effective Length): This is the length of the member that is considered for buckling analysis. It depends on the actual length of the member and its end support conditions (how it is restrained against rotation and translation). IS 800 provides guidelines and tables (e.g., Table 11 in IS 800:2007) for determining the effective length factor based on idealized support conditions. The effective length is calculated by multiplying the actual length (\(L\)) by the effective length factor (\(k\)), i.e., \(L_{eff} = kL\).
- \(r_{min}\) (Minimum Radius of Gyration): This is a geometric property of the cross-section of the member. It represents the distribution of the cross-sectional area around an axis. The minimum radius of gyration is used because buckling is most likely to occur about the axis for which the radius of gyration is minimum. It is calculated as \(r = \sqrt{\frac{I}{A}}\), where \(I\) is the moment of inertia about the axis and \(A\) is the cross-sectional area. The minimum value of \(r\) considering all possible axes (typically the principal axes) is used for the slenderness ratio calculation.
Controlling the slenderness ratio within permissible limits specified by codes like IS 800 is essential in steel design to prevent buckling, which is a sudden and often catastrophic failure mode for compression members, particularly long and slender ones. A lower slenderness ratio indicates a stockier member that is less susceptible to buckling.
Important Questions from Compression Member
The effective length of a battened strut of actual length L, effectively held in position both ends but not restrained in direction, is taken as
Which one of the following is a compression member?
The strength of compression members subjected to axial compression is defined by curves corresponding to _______ classes.
The double lacing shall be designed to resist transverse shear Vt equal to - (where P is total load acting on the column)
Which of the following members is/are subjected to compressive stress?
