An aluminium strut 10 ft long has a rectangular cross section 1.5in by 3 in. A bolt through each end secure the strut in such a way that is acts as hinged column about an axis perpendicular to 3 in dimension; and as fixed column about an axis perpendicular to 1.5 in dimension. Determine the safe central load with a factor of safety of 2 and E= 10300000 psi. Also discuss in detail about the governing column capacity and reasons behind it.

Q#.  An aluminium strut 10 ft long has a rectangular cross section 1.5in by 3 in. A bolt through each end secure the strut in such a way that is acts as hinged column about an axis perpendicular to 3 in dimension; and as fixed column about an axis perpendicular to 1.5 in dimension. Determine the safe central load with a factor of safety of 2 and E= 10300000 psi.

Also discuss in detail about the governing column capacity and reasons behind it.          

SOLUTION

L = 10 ft

   P safe =  ?   Fos = 2

 

  Moment of inertia ;

 Ix and Iy

Ix = bh³/12   ⇉  1.5(3)³/12 

    Ix = 3.37in⁴

rx = √Ix/A ⇉   √3.37/ 1.5 × 3  ⇉  0.86´´ 

    rx = 0.86in

 

Iy = bh³/12  ⇉   3 (1.5)³ / 12  = 0.843

    Iy= 0.843 in⁴

ry = √Iy/A = √ 0.843 / 1.5× 3 ⇉    0.483in

   ry = 0.483in

 

when moment is about  X- axis                            (    E= 10.3×10⁶;  and Le =120)

 hinsed = Le=L

 

 P = E Ix π ² / Le ²  ⇉    (10.3×10⁶ ) ×3.37× π ²  /(120)²                 

            P= 23790.5 lbs

                                     Psafe = 23790.5/2

                                  = 11895.25 lbs                                                   

 

 When moment is about to y-axis

P = E Iy π ² / Le ²  ⇉    (10.3×10⁶ ) ×0.843× π ²  /(0.5×120)²

 P=23780.53    ⇉   psafe= 23780.53/2

 

                                       psafe= 7934.88lbs  is governing value for colum capacity