## Answers

GIVEN STRUCTURE & DATA 8 kips 12 ft 10 kips 16 ft 20 ft 25 ft 15 ft Ratio of areas of columns 10 10 CALCULATIONS LOCATION OF CENTROID OF AREAS OF COLUMNS Taking summation of moments of areas of the columns about the left end column, 210 160 t 34 + 600 28.53 ft

AXIAL FORCES TOP STOREY 8 kips 20 15 25 P21 P22 P23 P24 A1 A2 28.53 25 A4 P22 8.53 P21 28.53 0.3 P21 P23 6.47 P21 28.53 0.23 P21 P24 31.47 P21 28.53 1.1 P21 Taking moment of the axial forces in the columns about the hinge point on the right end column, we have 6 -P2160 P22x40

P23 X 25 0 Solving, we get 0.62 kips 0.19 kips 0.14 kips -0.68 kips (tension) (tension) (compression) (compression) P21 P22 P23 P24 BOTTOM STOREY 12 ft 10 kips 8 ft P11 P12 P13 P14 8.53 P11' 28.53 P12 0.3 P11 6.47 P11 0.23 P11 31.47 P11 P13 28.53 P14 28.53 1.1 P11 Taking moment of the axial forces in the columns about the hinge point on the right end column, we have

10 20 P11 x60 P12 x40 P13 x 25- 0 Solving, we get P21 P22 P23 P24 3.09 kips 0.93 kips -0.71 kips 3.40 kips (tension) (tension) (compression) (compression) FREE BODY DIAGRAM 0.62 10 0.62 0.81 0.81 0.66 0.66 5 1215 10 12.5 6.97 6.97 39 4.929 4.929 2.539 6 1.03 2.041 2.39 539 0.14 0.62 0.19 0.68 0.62 0.19 0.14 0.68 1.03 2.041 2.39 2.539 2.47 10 3.21 3.21 6 2.47 2.64 2.64 10 7.5 7.5 2.5 10 8.715 8.715 6.19 6.19 3.23 3.23 4.566 5.769 2.315 5.35 3.09 0.93 0.71 3.399

FORCES IN FRAME MEMBERS 6.18 6.046 8.293 12.226 6.18 14.339 6.18 6.046 8.293 24.7 2636.548 24.074 08 6.1 18.52 14,339 33.815 4.08 24.7 24.074 24.08 18.5 8 33.8 24 Therefore, reactions at the base of the columns 3.09 kips 2.315 kips 18.52 ft.kips 0.93 kips 4.566 kips 36.548 ft.kips 3.40 kips 5.769 kips 24.08 ft.kips Axial Shear Moment 0.71 kips 5.35 kips 33.815 ft.kips

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