Question

HW#3 HWK 3: For the given frame, calculate the axial and shear forces and the moments in each member using: a) Portal Method b) Cantilever Method (Column Areas vary - see problem statement) 20 kips 14-09 Ops 160 17€ 140- - Ι - Ι - Ι Ι Area 23 22 15 32 1 of 1

Answer 1

GIVEN STRUCTURE & DATA 30 kips 14 ft 60 kips 14 ft K 14h * 175 # * 14h * CALCULATIONS TOP STOREY 30 kips * Η For equilibrium, Therefore, H+2H+2H+H = 30 H = 5

5 4.00 4.00 55 7 30 8.75 K K 1 8.75 k 8.75 ? 30 1.00 BOTTOM STOREY 30 kips 60 kips 2H For equilibrium, Therefore, H+2H+2H+H = 90 H = 15

1.00 1.00 101 20 20 16.00 16.00 20.00 20.00 8.75 8.75 7 SO 30 5.00 15.00 FORCES IN FRAME MEMBERS 70 140 2140 35105 210 = 210_ 35___105 140 1401 140 105 210 -

GIVEN STRUCTURE & DATA 30 kips 60 kips > 14 ft - 14th * 175 € * 144 Ratio of areas of columns 15.8 23.2 23.2 15.8 15.8 CALCULATIONS LOCATION OF CENTROID OF AREAS OF COLUMNS Taking summation of moments of areas of the columns about the left end column, 14 x 23.2 + x 23.2 + 46 x 15.8 31.5 78.0 22.75 ft

AXIAL FORCES i) TOP STOREY 30 kips 175 P21 P23 22.75 8.75 A4 8.75 P21 22.75 0.38 P21 8.75 P21 22.75 0.38 P21 P24 = 22.75 P21 22.75 1 P21 Taking moment of the axial forces in the columns about the hinge point on the right end column, we have 30 X 7 - P21 X 45.5 - P22 X 31.5 - P23 x 14 = 0

Solving, we get P21 P22 3.34 kips 1.27 kips -1.27 kips -3.34 kips (tension) (tension) (compression) (compression) P24 ii) BOTTOM STOREY 30 kips 14 ft 60 kips > 7 ft P11 P12 8.75 P11 22.75 0.38 P11 8.75 P11 22.75 0.38 P11 P14 = 22.75 P11 22.75 1 P11 Taking moment of the axial forces in the columns about the hinge point on the right end column, we have 30 X 21 60 X 7 - P11 X 45.5 - P12 X 31.5 . P13 x 14 = 0

FORCES IN FRAME MEMBERS 23.38 40.32 23.38 63.7 63.7 23.38 23.38 1 40.32 23.38 / 93.66 191.52 A161.56 63.7 259.42 161.6 161.6 23.381 70.28 63.7 93.66 161.56 161.56 70.28 191.52 259.42 161.56 Therefore, reactions at the base of the columns: Axial Shear Moment 16.72 kips 10.04 kips 70.28 ft.kips 6.35 kips 27.36 kips 191.52 ft kips 6.35 kips 27.36 kips 259.42 ft.kips 16.72 kips 25.24 kips 161.56 ft.kips