Column Analogy Method 10

8B 2 1I 6 C

4 1I 1I 4X X

A D

Frame Properties:

Height of AB = 4 m Load P Value = 10 kNLength of BC = 8 m Left length of Load = a 2 mHeight of CD = 4 m Right length of Load = b 6 m

Analogous Column Properties:Thickness of Analogous column, BC = 1 IThickness of Analogous column, AB = 1 IThickness of Analogous column, CD = 1 IMoI of the analogous column section about the centroidal axis XX = 27.33 unitsMoI of the analogous column section about the centroidal axis YY = 141.33 units

Properties of Load Diagram:Max. Bending Moment = P.ab/l = 15 kN-mDistance of the centroid of the section from AB =(L+a)/3 = 3.33 mDistance of the centroid of the section from BC = 1 mArea of Analogous Column, A = 16 UnitsTotal Load On Analogous Column = Vol. of the load diagram 60 kN

1 m

0.67 m

60.00

40.00

Stress Calculation:

-5.88 kN/m

12.25 kN/m

12.81 kN/m

-4.18 kN/mFinal Moment :

Eccentricity of load from the axis XX,exx =

Eccentricity of load from the axis YY ,eyy=

Moment at X-X axis, Mxx =

Moment at Y-Y axis, Myy =

Stress at A ; Mia = P/A -(Myy/Iyy).Y-(Mxx/Ixx).X

Stress at B ; Mib= P/A - (Myy/Iyy).Y+(Mxx/Ixx).X

Stress at C ; Mic = P/A + (Myy/Iyy).Y+(Mxx/Ixx).X

Stress at D ; Mid = P/A + (Myy/Iyy).Y-(Mxx/Ixx).X

5.88 kN/m

-12.25 kN/m

-12.81 kN/m

4.18 kN/m

Ma = Msa-Mia =

Mb = Msb-Mib =

Mc = Msc-Mic =

Md = Msd-Mid =