Question

The W200 x 46 A36 steel column is pinned at its top and fixed at its base. The column is braced at its mid-height against the weak axis. Figure Q3 shows the side view of column in x-x axis. Given the cross-sectional area of steel column A = 5890 mm$^2$, moment of inertia in x-axis $I_x = 45.5 \times 10^{-4}$ m$^4$, moment of inertia in y-axis $I_y = 15.3 \times 10^{-6}$ m$^4$, yielding stress $\sigma_Y = 250$ MPa and modulus of elasticity $E = 200$ GPa. 5 m 5 m Figure Q3 (i) Calculate the critical buckling loads in both axis. (12 marks) (ii) Compare the critical buckling loads from Q3(b)(i) and identify the maximum axial load that the column can support without causing it to buckle. (3 marks) (iii) Calculate the critical stress using the Euler's formula, and compare with the yielding stress to indicate the critical strength. (5 marks) [Total : 25 marks]

          The W200 x 46 A36 steel column is pinned at its top and fixed at its base. The
column is braced at its mid-height against the weak axis. Figure Q3 shows the
side view of column in x-x axis. Given the cross-sectional area of steel column
A = 5890 mm$^2$, moment of inertia in x-axis $I_x = 45.5 \times 10^{-4}$ m$^4$, moment of
inertia in y-axis $I_y = 15.3 \times 10^{-6}$ m$^4$, yielding stress $\sigma_Y = 250$ MPa and modulus
of elasticity $E = 200$ GPa.

5 m

5 m

Figure Q3
(i) Calculate the critical buckling loads in both axis. (12 marks)
(ii) Compare the critical buckling loads from Q3(b)(i) and identify the
maximum axial load that the column can support without causing it to
buckle. (3 marks)
(iii) Calculate the critical stress using the Euler's formula, and compare
with the yielding stress to indicate the critical strength. (5 marks)
[Total : 25 marks]

The W200 x 46 A36 steel column is pinned at its top and fixed at its base. The
column is braced at its mid-height against the weak axis. Figure Q3 shows the
side view of column in x-x axis. Given the cross-sectional area of steel column
A = 5890 mm^2, moment of inertia in x-axis Ix = 45.5 × 10^-4 m^4, moment of
inertia in y-axis Iy = 15.3 × 10^-6 m^4, yielding stress = 250 MPa and modulus
of elasticity E = 200 GPa.

5 m

5 m

Figure Q3
(i) Calculate the critical buckling loads in both axis. (12 marks)
(ii) Compare the critical buckling loads from Q3(b)(i) and identify the
maximum axial load that the column can support without causing it to
buckle. (3 marks)
(iii) Calculate the critical stress using the Euler's formula, and compare
with the yielding stress to indicate the critical strength. (5 marks)
[Total : 25 marks]

Added by Jesse S.

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