In solving the problems of Section 10.3, assume that the compression member in question is an ideal slender; prismatic, elastic column with the stated end conditions. Also, assume that defections and slopes are small.

Determine the elastic buckling load of a 12-ft- long 6 x 6 timber column that can be considered to be fixed at its base and free at the top. Let the modulus of elasticity (in compression parallel to the grain) be Est = 1.6(103) ksi, and let ?Y = 6 ksi. (Recall that the fnished dimensions of the wood column are smaller than the nominal dimensions stated above. See Table 0.8 of Appendix

D-)

Table D.8: Properties of Structural Lumber* (U.S. Customary Units)

*$4$ = surfaced four sides,

All properties and weights are for dressed lumber sizes.

Specific weight = 35 lb/n ³ .

Axes 1 ? 1 and 2 ? 2 are principal ceotroidal axes.

Based on a table cumpiled by the National Forest Products Association.

Transcribed Image Text:

Fig. P10.3-8 12 ft -6x6 Sectional properties of American Standard Lumber (S4S)* Axis 1-1 Nominal Dimensions in. 2x4 2x6 2x8 2x10 2x12 3x4 3x6 3x8 3x10 3x12 4X4 4X6 4x8 4x10 4x12 6x6 6x8 6x10 6X12 8x8 8X10 8x12 Net Dimensions bxh 1.5x3.5 1.5x5.5 1.5x7.25 15x9.25 1.5x11.25 2.5x3.5 2.5x5.5 25x7.25 25x9.25 25x11.25 3.5x3.5 3.5x5.5 3.5x7.25 35x9.25 3.5x11.25 5.5x5.5 5.5x7.5 55x9.5 5.5x11.5 75x75 75×95 7.5x11.5 Area A = Nir in 5.25 8.25 10.88 13.88 16.88 8.75 13.75 18.13 23.13 28.13 12.25 19.25 25.38 32.38 39.38 30.25 41.25 52.25 63.25 56.25 71.25 86.25 Moment of Inertia 5.36 20.80 47.63 98.93 177.98 8.93 34.66 79.39 164.89 296.63 12.51 48.53 111.15 230.84 415.28 76.3 193.4 393.0 697.1 263.7 535.9 950.5 Section Modulus 3.06 7.56 13.14 21.39 31.64 5.10 12.60 21.90 35.65 52.73 7.15 17.65 30.66 49.91 73.83 27.7 51.6 82.7 121.2 70.3 112.8 165.3 Axis 2-2 Moment of Inertial 0.98 1.55 2.04 2.60 3.16 4.56 7.16 9.44 12.04 14.65 12.51 19.65 25.90 33.05 40.20 76.3 104.0 131.7 159.4 263.7 334.0 404.3 Section Modulus S₂-² 1.31 2.06 2.72 3.47 4.22 3.65 5.73 7.55 9.64 11.72 7.15 11.23 14.80 18.89 22.97 27.7 37.8 47.9 58.0 70.3 89.1 107.8 Weight per Lineal Foot Ib 1.3 2.0 26 3.4 2.1 3.3 5.6 6.8 3.0 4.7 6.2 7.9 9.6 7.4 10.0 12.7 15.4 13.7 17.3 21.0 Fig. P10.3-8 12 ft -6x6 Sectional properties of American Standard Lumber (S4S)* Axis 1-1 Nominal Dimensions in. 2x4 2x6 2x8 2x10 2x12 3x4 3x6 3x8 3x10 3x12 4X4 4X6 4x8 4x10 4x12 6x6 6x8 6x10 6X12 8x8 8X10 8x12 Net Dimensions bxh 1.5x3.5 1.5x5.5 1.5x7.25 15x9.25 1.5x11.25 2.5x3.5 2.5x5.5 25x7.25 25x9.25 25x11.25 3.5x3.5 3.5x5.5 3.5x7.25 35x9.25 3.5x11.25 5.5x5.5 5.5x7.5 55x9.5 5.5x11.5 75x75 75×95 7.5x11.5 Area A = Nir in 5.25 8.25 10.88 13.88 16.88 8.75 13.75 18.13 23.13 28.13 12.25 19.25 25.38 32.38 39.38 30.25 41.25 52.25 63.25 56.25 71.25 86.25 Moment of Inertia 5.36 20.80 47.63 98.93 177.98 8.93 34.66 79.39 164.89 296.63 12.51 48.53 111.15 230.84 415.28 76.3 193.4 393.0 697.1 263.7 535.9 950.5 Section Modulus 3.06 7.56 13.14 21.39 31.64 5.10 12.60 21.90 35.65 52.73 7.15 17.65 30.66 49.91 73.83 27.7 51.6 82.7 121.2 70.3 112.8 165.3 Axis 2-2 Moment of Inertial 0.98 1.55 2.04 2.60 3.16 4.56 7.16 9.44 12.04 14.65 12.51 19.65 25.90 33.05 40.20 76.3 104.0 131.7 159.4 263.7 334.0 404.3 Section Modulus S₂-² 1.31 2.06 2.72 3.47 4.22 3.65 5.73 7.55 9.64 11.72 7.15 11.23 14.80 18.89 22.97 27.7 37.8 47.9 58.0 70.3 89.1 107.8 Weight per Lineal Foot Ib 1.3 2.0 26 3.4 2.1 3.3 5.6 6.8 3.0 4.7 6.2 7.9 9.6 7.4 10.0 12.7 15.4 13.7 17.3 21.0

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Determine the elastic buckling load of a column which is fixed at its base and free at the ... View the full answer