WORLD FOR CIVIL

7.6c Columns & Buckling - Topic Examination

1. A 16 foot long wood 2" by 6" is used as a fixed-fixed column. Young's modulus for the wood is 2 x 10 ⁶ lb/in². Determine: a) the slenderness ratio; b) the Euler buckling load; c) the axial stress in the column when the Euler load is applied.

2. A W10x29 steel I-Beam, 18 ft long, is to be used as a column with pinned-pinned ends. Young's modulus for the steel is 30 x 10 ⁶ lb/in², and the allowable axial stress for the steel is 45,000 psi. Determine the load which will cause the beam to buckle. [Hint: Determine the slenderness ratio. Then use the Euler formula if it is a long column or the J.B. Johnson formula (see below) is it is an intermediate column.] The beam characteristics are listed below.

-	-	-	Flange	Flange	Web	Cross	Section	Info.	Cross	Section	Info.
Designation	Area	Depth	Width	thick	thick	x-x axis	x-x axis	x-x axis	y-y axis	y-y axis	y-y axis
-	A-in2	d - in	wf - in	tf - in	tw - in	I - in4	S -in3	r - in	I - in4	S -in3	r - in
W 10x29	8.54	10.22	5.799	0.500	0.289	158.0	30.8	4.30	16.30	5.61	1.38

J.B. Johnson's formula:

C (critical slenderness ratio) :

3. Copper water pipe in a house is 1.5 inches in diameter with 1/16 inch walls. The allowable tensile stress in the copper is 8000 psi. Determine the maximum pressure that the pipes can withstand.

4. Select the best (safe and lightest) structural steel I-beam to be used as a fixed-free column of length 16 feet which is to carry a load of 300,000 lb. The yield stress of the steel is 42,000 psi. (See tables below). E_steel = 30 x 10⁶ psi.

-	-	-	Flange	Flange	Web	Cross	Section	Info.	Cross	Section	Info.
Designation	Area	Depth	Width	thick	thick	x-x axis	x-x axis	x-x axis	y-y axis	y-y axis	y-y axis
-	A	d	wf	tf	tw	I	S	r	I	S	r
-	in2	in	in	in	in	in4	in3	in	in4	in3	in
W 5x18.5	5.43	5.12	5.025	0.420	0.265	25.4	9.9	2.16	8.89	3.54	1.28
W 6x16	4.72	6.25	4.030	0.404	0.260	31.7	10.2	2.59	4.42	2.19	0.97
W 6x25	7.35	6.37	6.080	0.456	0.320	53.3	16.7	2.69	17.10	5.62	1.53
W 8x67	19.70	9.00	8.287	0.933	0.575	272.0	60.4	3.71	88.60	21.40	2.12
W 10x29	8.54	10.22	5.799	0.500	0.289	158.0	30.8	4.30	16.30	5.61	1.38
W 10x45	13.20	10.12	8.022	0.618	0.350	249.0	49.1	4.33	53.20	13.30	2.00
W 12x22	6.47	12.31	4.030	0.424	0.260	156.0	25.3	4.91	4.64	2.31	0.85
W 12x36	10.60	12.24	6.565	0.540	0.305	281.0	46.0	5.15	25.50	7.77	1.55
W 14x38	11.20	14.12	6.776	0.513	0.313	386.0	54.7	5.88	26.60	7.86	1.54
W 14x74	21.80	14.19	10.072	0.783	0.450	797.0	112.0	6.05	133.00	26.50	2.48
W 14x136	40.00	14.75	14.740	1.063	0.660	1590.0	216.0	6.31	568.00	77.00	3.77
W 14x426	125.00	18.69	16.695	3.033	1.875	6610.0	707.0	7.26	2360.00	283.00	4.34
W 16x50	14.70	16.25	7.073	0.628	0.380	657.0	80.8	6.68	37.10	10.50	1.59
W 16x96	28.20	16.32	11.533	0.875	0.535	1360.0	166.0	6.93	224.00	38.80	2.82
W 18x60	17.70	18.25	7.558	0.695	0.416	986.0	108.0	7.47	50.10	13.30	1.68
W 21x73	21.50	21.24	8.295	0.740	0.455	1600.0	151.0	8.64	70.60	17.00	1.81
W 24x94	27.70	24.29	9.061	0.872	0.516	2690.0	221.0	9.86	108.00	23.90	1.98
W 27x114	33.60	27.28	10.070	0.932	0.570	4090.0	300.0	11.00	159.00	31.60	2.18
W 33x240	70.60	33.50	15.865	1.400	0.830	13600.0	813.0	13.90	933.00	118.00	3.64
W 36x300	88.30	36.72	16.655	1.680	0.945	20300.0	1110.0	15.20	1300.00	156.00	3.83