Structural and Stress Analysis 3rd. Edition by Megson, T.H.G. | 9780080999364 | 0080999360

Structural Analysis

Structural and Stress Analysis

579 SOLVED PROBLEMS

1 SOLVED PROBLEMS

Question: 20.5

A simply supported beam AB has a span of 5 m and carries a uniformly distributed dead load of 0.6 kN/m (Fig. 20.12(a)). A similarly distributed live load of length greater than 5 m and intensity 1.5 kN/m travels across the beam. Calculate the length of beam over which reversal of shear force occurs ...

Verified Answer:

The shear force at a section of the beam will be a...

Question: 20.4

A load of length 2 m and intensity 2 kN/m crosses the simply supported beam AB shown in Fig. 20.9(a). Calculate the maximum positive and negative values of shear force and the maximum value of bending moment at the quarter span point. ...

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The shear force and bending moment influence lines...

Question: 21.P.16

A tubular column of length L is tapered in wall thickness so that the area and the second moment of area of its cross section decrease uniformly from A1 and I1 at its centre to 0.2A1 and 0.2I1 at its ends, respectively. Assuming a deflected centreline of parabolic form and taking the more correct ...

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Assume the equation of the deflected centre line o...

Question: 21.P.15

A pin-ended column of length L has its central portion reinforced, the second moment of its area being I2 while that of the end portions, each of length a, is I1. Use the Rayleigh-Ritz method to determine the critical load of the column assuming that its centreline deflects into the parabola υ = kx ...

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The bending moment at any section of the column is...

Question: 21.P.14

A mild steel pin-ended column is 2.5 m long and has the cross section shown in Fig. P.21.14. If the yield stress in compression of mild steel is 300 N/mm² , determine the maximum load the column can withstand using the Robertson formula. Compare this value with that predicted by the Euler theory. ...

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The column will buckle about an axis parallel to i...

Question: 21.P.13

A column is fabricated from two 250 mm × 75 mm channel sections attached to two flange plates each 300 mm × 12 mm as shown in Fig. P.21.13; the column height is 10 m and the ends of the column are fixed. If the yield stress of mild steel in compression is 250 N/mm² use the Perry-Robertson formula ...

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By inspection and by comparison with S.21.11 the c...

Question: 21.P.12

A column is fabricated from two 305 mm × 305 mm × 158 kg Universal Column sections placed side by side as shown in Fig. P.21.12. The column has fixed ends and an overall height of 12 m. Given that the yield stress in compression of mild steel is 250 N/mm² calculate the maximum allowable load for ...

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The second moment of area about the axis of symmet...

Question: 21.P.11

A mild steel column is 6 m long, is fixed at both ends and has the cross section shown in Fig. P.21.11. Given that the yield stress in compression of mild steel is 300 N/mm² calculate the maximum allowable load for the column using the Perry-Robertson formula. Take E = 200000 N/mm² and assume a ...

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The column will buckle about an axis along the lin...

Question: 21.P.10

A short length of hollow tube 32 mm external diameter and 25 mm internal diameter yielded in a compression test at a load of 70 kN. When a 2.5 m length of the same tube was tested as a column with fixed ends the failure load was 24.1 kN. Assuming that σS in the Rankine formula is given by the first ...

Verified Answer:

In Eq. (21.27)

P=\frac{\sigma_{S} A}{1+k\le...

Question: 21.P.9

A tubular column has an effective length of 2.5 m and is to be designed to carry a safe load of 300 kN. Assuming an approximate ratio of thickness to external diameter of 1/16, determine a practical diameter and thickness using the Rankine formula with σs = 330 N/mm² and k = 1/7500. Use a safety ...

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The second moment of area of the column is given b...

Question: 8.8

A straight uniform column of length l and bending stiffness EI is subjected to uniform lateral loading w/unit length. The end attachments do not restrict rotation of the column ends. The longitudinal compressive force P has eccentricity e from the centroids of the end sections and is placed so as ...

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Referring to Fig. S.8.8, the bending moment at any...