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3a) Calculate the safe compressive load on a hallow steel column of one end rigidly fixed and other end hinged with 12 cm external diameter and 8 cm internal diameter and 10 m length. Use Euler's formula with a factor of safety 3 and E = 200 GPa.?
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3a) Calculate the safe compressive load on a hallow steel column of on...
Calculating Safe Compressive Load on a Hollow Steel Column

Given Data:
- External diameter (D) = 12 cm
- Internal diameter (d) = 8 cm
- Length of the column (L) = 10 m
- Factor of safety (FoS) = 3
- Young's modulus of steel (E) = 200 GPa = 200 x 10^9 Pa

Calculating the Effective Length of the Column (Le):
Effective length, Le = Length of the column (L)
Le = 10 m = 1000 cm

Calculating the Slenderness Ratio (λ):
Slenderness ratio, λ = Le / r
where r is the radius of gyration
r = √(D^2 + d^2) / 4
r = √((12^2 + 8^2) / 4) = √(208) ≈ 14.42 cm
λ = 1000 / 14.42 ≈ 69.36

Calculating the Critical Stress (σc):
Critical stress, σc = (π^2 x E) / (λ^2)
σc = (π^2 x 200 x 10^9) / (69.36^2)
σc ≈ 10.17 x 10^9 Pa

Calculating the Safe Load:
Safe load, P = (π^2 x E x I) / (Le)^2
where I is the moment of inertia of the column
I = π/64 x (D^4 - d^4)
I = π/64 x ((12^4 - 8^4) = π/64 x 3136 = 49π cm^4
P = (π^2 x 200 x 10^9 x 49π) / 1000^2
P ≈ 96.4 x 10^6 N

Applying Factor of Safety:
Safe compressive load = P / FoS
Safe compressive load ≈ 96.4 x 10^6 / 3
Safe compressive load ≈ 32.13 x 10^6 N
Therefore, the safe compressive load on the hollow steel column is approximately 32.13 MN.
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Accountability, or the lack of it, in governance generally, and civil services, in particular, is a major factor underlying the deficiencies in governance and public administration. Designing an effective framework for accountability has been a key element of the reform agenda. A fundamental issue is whether civil services should be accountable to the political executive of the day or to society at large. In other words, how should internal and external accountability be reconciled? Internal accountability is sought to be achieved by internal performance monitoring, official supervision by bodies like the —Central-Vigilance Commission-andComptroller and Auditor—General, and judicial review of executive decisions. Articles 311 and 312 of the Indian Constitution provide job security and safeguards to the civil services, especially the All India Services. The framers of the Constitution had envisaged that provision of these safeguards would result in a civil service that is not totally subservient to the political executive but will have the strength to function in larger public interest. The need to balance internal and external accountability is thus built into the Constitution. The issue is where to draw the line. Over the years, the emphasis seems to have tilted in favour of greater internal accountability of the civil services to the political leaders of the day who in turn are expected to be externally accountable to the society at large through the election process. This system for seeking accountability to Society has not worked out, and has led to several adverse consequences for governance.Some special measures can be considered for improving accountability in civil services.Provisions of articles 311 and 312 should be reviewed and laws and regulations framed to ensure external accountability of civil services. The proposed Civil Services Bill seeks to address some of these requirements. The respective roles of professional civil services and the political executive should he defined so that professional managerial functions and management of civil services are depoliticized. For this purpose, effective statutory civil service boards should be created at the centre and in the states. Decentralization and devolution of authority to bring government and decision making closer to the people also helps to enhance accountability.Q. Which one of the following is the essential message implied by this passage?

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3a) Calculate the safe compressive load on a hallow steel column of one end rigidly fixed and other end hinged with 12 cm external diameter and 8 cm internal diameter and 10 m length. Use Euler's formula with a factor of safety 3 and E = 200 GPa.?
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