Allowable load in short compression member

[whereitsbeen]

My apologies, I don't own a scanner or else I would show the 200 variations of formulas I've played around (my work) with all day to get these answers.

Question is this;
A short compression member is fabricated from 2 steel pipes. the pipe on the top has a cross sectional area of 3.17 in sq and is 4" long. The pipe on the bottom has a cross sectional area of 5.53 in sq and is 6" long.
Each pipe has a downward force at the centre-top of each pipe.
The allowable compressive stress in the steel is 21.6 ksi.
a) What is the allowable load in the bottom pipe if the load in the top pipe is 22 kips?
b) What is the allowable load in the top pipe if the load in the bottom pipe is 40 kips?

the answer for a) is 97.4 kips and b) is 68.5 kips.

I've tried most stress formulas but there must be something I am missing. If you're able to show guidance, I'd appreciate the help. Thanx
-M

 

[SteamKing]

Draw a free body diagram of your problem and add the given forces. (Hint: with such short pieces of pipe, buckling instability can be ignored.) Use the allowable stress to determine the unknown load.

 

[whereitsbeen]

for b, I get 21600 x 317 = 68.5 which is good

for a, I get 21600 x 5.53 = 119.4 which is no good

 

[SteamKing]

Did you draw the FBD? Notice, the pipes with the unknown loads are in different locations for a) and b).