WORLD FOR CIVIL

Topic 7.4: Columns & Buckling - Topic Examination

1. A large steel pipe is used as a pinned-pinned column. The pipe is 18 feet long with an outer diameter of 6 inches and an inner diameter of 5 inches. Young's modulus is 30 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.
The radius of gyration of hollow circular area: r = [sqrt (d_o² + d_i²)] / 4 ; Moment of Inertia: I = [pi * (d_o⁴ - d_i⁴)] / 64
[a) 111; b) 209,030 lb; c) 24,200 psi.]

2. A 20 foot long WT 12 x 42 steel T-beam is used as a fixed - free column. Determine the slenderness ratio, the Euler Buckling load, and the axial stress when the Euler Buckling load is applied. Young's modulus is 30 x 10 ⁶ lb/in². [radius of gryration about y-y axis = 1.95"; moment of inertia about y-y axis = 47.2 in⁴; area = 12.4 in²]
[a) 246; b) 60,660 lb.; c) 4,890 psi.]

3. A W 8x40 aluminum 6061 -T6 alloy I-beam is used as a pinned-pinned column. Determine the maximum allowable length permittted if a load of a) 50,000 lb is applied., and if a load of b) 100,000 lb is applied. See table below. [ a) 18.65 ft.; b) 13.2 ft.]

-	A-in2	d - in	wf - in	tf - in	tw - in	Ixx - in4	Sxx -in3	rxx- in	Iyy - in4	Syy -in3	ryy - in
W8x40	11.80	8.25	8.077	0.558	0.365	146.0	35.5	3.53	49.00	12.10	2.04

4. Select the best (safe and lightest) structural streel I-beam to be used as a pinned-pinned column of length 20 feet which is to carry a load of 60,000 lb. The yield stress of the steel is 36,000 psi. (See tables below)
[More than one beam may work well. The W12 x 36 gives a maximum load of 68,000 lb, with an allowable buckling stress of 6,420 psi for the 20 ft beam with a allow steel stress of 36,000 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
-	A-in2	d - in	wf - in	tf - in	tw - in	I - in4	S -in3	r - in	I - in4	S -in3	r - in
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