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Slenderness ratio and axial load of steel question..pls help 
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#1
Jul406, 02:57 AM

P: 6

Hi, I have the following question to complete and i was wondering if anyone can help..
Compare the slenderness ratio and maximum safe axial load that a universal column of section 152 x 152 x 37 can carry if it is made from grade 43 steel to BS5950; 1985 and 6.5m in height when its ends are fixed as follows: a) both ends pinjointed, and b) one end directionfixed and other end pinjointed. i know the effective length for both ends pinjointed is l=L and one end direction_fixed, other pinjointed is l=0.85L. I have to use that with the formula: S.R = l/k where S.R is slenderness ratio, l= effective length and k = least radius of gyration. I also have these formulae: I=k²A where I = second moment of area, k= radius of gyration and A = crosssectional area. F=σA where F= safe axial load, σ= allowable stress and A=cross sectional area I also got a table from BS5950:Part 1:1985 that shows the British Standards recommendations for allowable slendreness ratio If anyone could help i would appreciate it greatly thanx in advance 


#2
Jul406, 06:44 AM

Sci Advisor
P: 5,095

Your question makes little sense.



#3
Jul506, 10:10 AM

P: 6

Hi Fred, thanks for replying to my post. however, that is exactly how the question is written word for word.
Compare the slenderness ratio and maximum safe axial load that a universal column of section 152 x 152 x 37 can carry if it is made from grade 43 steel to BS5950; 1985 and 6.5m in height when its ends are fixed as follows: a) both ends pinjointed, and b) one end directionfixed and other end pinjointed. thanx 


#4
Jul506, 10:33 AM

Sci Advisor
P: 5,095

Slenderness ratio and axial load of steel question..pls help
The only thing I am wondering is in the dimensions of the column. You give 152x152x37. Is the 37 a wall thickness since you give the height as 6.5m? I am assuming so.
For some reason I read that problem about 20 times and it didn't click. Now it is. Perhaps I needed more coffee. So are you wondering where to start? Basically, you are looking at a change in restraints for two scenarios. Since the cross section doesn't change, the radius of gyration will not change. So, you have 2 boundary conditions. That means you should calculate the maximum safe load for 2 situations (4 if the BS spec also specifies a different material than the grade 43). Since I don't have access to the BS spec you referenced, I would assume that it spells out some minimums in the safe load. Take your 2 results and then compare them to the spec. It would be a lot easier to help if you had some specific questions. 


#5
Jul506, 05:11 PM

P: 6

thanx for your reply... i was sort of stuck on the dimensions aswell. I have done the following calculations and they do fall in the table i got but if i could run it past you could you tell me if it makes sense. here it is:
I=bd³/12 = 37 x 152³/12 = 11.93 x 106mm4(sorry i dont have a "ten to the power of 6"symbol) A=152 x 37 = 5624 mm² K=√I/A = √11930000/5624 = 46mm for a) both ends pinjointed l=L =1x6.5 = 6.5m = 6.5 x 10³ mm S.R=l/K = 6.5 x 10³/46 = 141.3 for b) one end directionfixed and other end pinjointed l=L =0.85 x 6.5 = 5.5m = 5.5 x 10³ mm S.R=l/K = 5.5 x 10³/46 = 119.5 on the table i got for slenderness ratio of 140 the allowable stress for flange thickness 17  40 mm is 83 for slenderness ratio of 120 the allowable stress for flange thickness 17  40 mm is 107 does this sound like im on the right track here? thanks for your help 


#6
Jul506, 05:24 PM

Sci Advisor
P: 5,095

Reexamine your calculation for the area. If it is a square hollow column, you'll need to subtract the area of the smaller area from the area of the larger.



#7
Jul606, 11:16 AM

P: 6

Ok.. ive got some figures from the british standards universal column table. it isnt hollow but is an "H" column. so...
for serial size 152 x 152 x 37: Cross sec. area (A) = 47.1cm = 471mm² Radius of gyration (k) = 38.7mm so slenderness ratio for a): S.R = l/k = 6.5 x 10³/38.7 = 168 for flange thickness of 11.5 the allowable stress is 62 Nmm² and for b): S.R = l/k = 5.5 x 10³/38.7 = 142 for flange thickness of 11.5 the allowable stress is 83 Nmm² then the maximum safe axial load for a): F=ơA = 62 x 471 = 29202N = 29KN and for b): F=ơA = 83 x 471 = 39093N = 39KN does this sound like it to you? once again thanx very much 


#8
Jul606, 11:17 AM

P: 6

Ok.. ive got some figures from the british standards universal column table. it isnt hollow but is an "H" column. so...
for serial size 152 x 152 x 37: Cross sec. area (A) = 47.1cm = 471mm² Radius of gyration (k) = 38.7mm so slenderness ratio for a): S.R = l/k = 6.5 x 10³/38.7 = 168 for flange thickness of 11.5 the allowable stress is 62 Nmm² and for b): S.R = l/k = 5.5 x 10³/38.7 = 142 for flange thickness of 11.5 the allowable stress is 83 Nmm² then the maximum safe axial load for a): F=ơA = 62 x 471 = 29202N = 29KN and for b): F=ơA = 83 x 471 = 39093N = 39KN does this sound like it to you? once again thanx very much 


#9
Jul606, 11:26 AM

Sci Advisor
P: 5,095

I would believe those numbers. It looks like you have the right approach. I do have to ask where did your flange thickness of 11.5mm came from?
Now ask yourself if the two end allowable load results make sense to you. 


#10
Jul606, 01:09 PM

P: 6

I got the 11.5mm flange thickness from the same british standards table for that particular column.
do you mean by the two end results as in the 29N and the 39N or do each of the results make sense with how they are fixed (both pinjointed, etc...)? 


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