8 - Statics 293 PROBLEMS 8.1 The Pateenter in Princeton NJ...

Unformatted text preview: Statics -- 293 PROBLEMS 8.1 The Pateenter in Princeton, NJ is a large open structure with a cable-stayed roof as Show in Fig. P8.l. This figure shows one of the nine tubular steel masts that are uniformly spaced at 9 m intervals to support the roof structure. In this design, the roof hangs from cables because the verticalside members are used only to prevent wind uplift. The tubular mast, 15 m high, is supported with a 9 m wide by 6 m high rectangular steel flame. Determine the force in the primary rod stay and the tubular steel mast if the uniformly distributed load on the roof is 85 kN/m. Assume the roof is pinned to the steel mast at point C. Refer to the Example 8.3 in the text for additional dimensions. RING CONNECTOR SECONDARY ROD STAYS VERTICAL MEMBER TO PREVENT WIND UPLIFT Fig. P8.1 8.2 A new building similar to the Pateenter is under consideration by an architectural firm. They propose increasing the height of the mast from 15 m to 24 m to make the appearance of the structure more dramatic. If all of the other parameters are the same as given in Problem 8.1, prepare an analysis indicating the effect of this change. 8.3 A new building similar to the Pateenter is under consideration by an architectural firm. They propose a structure with the dimensions presented in Fig. P83. Determine the force in the primary rod stay AB and the tubular steel mast AC. Also find the reaction forces at point C. Fig. P83 6m 28m 294 ~—— Chapter 8 Space Strnctures and 3—D Equilibrium 8.4 A space truss, shown in Fig. P84, is supported at point A with a ball and socket joint and with cables anchored at points B and D. A force F is ‘ applied to joint E. if F is represented in vector format as shown in Fig. P84, determine the internal forces in the three members that intersect at joint E. Also Specify the diameter of the rods, if the truss is fabricated from a 1018 A ‘ steel alloy. A safety factor of SF : 4.0 based on yield strength is specified by the building code. The truss dimensions are given in ft. Fig. PM a Determine the internal forces in members AB, ANCHOR DB and EB of the truss described in Problem PO'NTS 8.4. 8.6 Determine the internal forces in members AC, DC and EC of the truss described in Problem 8.4. 8.7 For the communications tower illustrated in Fig. P8.7, a wind force of 3,500 lb from the West is applied at a position 2 = 300 ft. The tower has a height H = 400 ft and a dead weight W 2% = 40 hips. The anchor points on the ground E plane are defined by: X; = lOOft, X2 = 115 ft, ' y1 = 130 ft and yz = 145 ft. The cables have a breaking strength of 29,200 lb and a ball and socket joint is used to support the tower at point 0. Determine the loads in the four cables and the reaction forces at the base of ANCHOR the tower. Also determine the minimum PO'NT safety factor. Fig. 398.7 The anchor points on the ground plane for the communications tower, shown in Fig. 138.7, ' GROUND are changed to: x1 = 60 m, x; = 70 m, y1 = 80 PLANE m, 3/2 = 90 m. The tower has a height of 120 in, a dead weight of 240 RN and is subjected to a wind force of 10.5 kN from the East, that is applied at a position 2 = 80 m. The cables have a breaking strength of 115 kN, and the tower is supported by a ball and socket joint at point 0. Determine the loads on the four cables and the reaction forces at the ball and socket joint. Also find the minimum safety factor. Statics — 295 8.9 If the steel used in fabrlcatmg the tower, described in Problem 8.7, has a yield strength of 45 ksi, determine the cross sectional area required at the base of the tower. The safety factor for the tower is specified as 6.5. Does the wind loading condition affect the result? 8.10 If the steel used in fabricating the tower, in Problem 88, has a yield strength of 320 MPa, determine the cross sectional area required at the base of the tower. The safety factor for the tower is specified as 5.5. Does the wind loading condition affect the result? 8.11; The safety factors for the communications tower, described in Problems 8.9 and 8.10, are very large. Develop arguments supporting the use of relatively large safety factors in the design of communications towers. Also develop arguments for redesign with smaller diameter cable, smaller footprint and smaller cross sectional area at the base of the tower structure. 8.12 A severe ice storm strikes the communications tower coating all of the members with a thick layer of ice. The dead weight of the tower is increased from 240 kN to 350 kN. Determine the decrease in the safety factor for the conditions of Problem 8.8. 8.13 For the derrick shown in Fig. P813 determine the margin of safety for the three cables if the DERRICK POLE SLEEVE ‘ BEARING BALL AND V‘ SOCKET BEAR NG Fig. P813 Fig. P8.13a 296 ——- Chapter 8 Space Structures and 3-D Equilibrium 8.14 A tetrahedral space truss, shown in Fig. P814, supports a massive scoreboard and several sets of remotely controlled spotlights in an ANCHOR amphitheater. The base ABC of the space truss POTS y lies in the X—y plane (horizontal). The base triangle is connected to anchors in the roof beams by long cables. Determine the size of the solid round rods that are required to fabricate members AB, AC and AD of the space truss. The safety factor based on yield strength is specified as 8.0. 1020 HR steel is employed for all of the members and the weight of the scoreboard and spotlights is 25.0 kN. SCOREBOARD Fig. P814 AND SPOTLIGHTS 8.15 For the long horizontal boom of a construction crane, illustrated in Fig. P815, determine the internal forces in the members AB, BF, BK, FG, KL and FL. The load applied to the boom is F = 12 kip. See Example 8.8 in the text for additional details. Fig. P815 8.16 Repeat Problem 8.15, if the loading on the long horizontal boom is increased from 12 kip to 15 kip. 8.17 A hanging light assembly is positioned near the corner of a gymnasium, as shown in Fig. P8.17. Determine the gage of the stainless steel wire required for the support of a light assembly weighing 1,500 N if a safety factor of 4.0 is specified. The wire is fabricated from 302A stainless steel. Points B and C are anchors that lie in the x-y plane and point D is an anchor that lies along the z—axis. Point A is not anchored; however, it lies in the x-y plane. LIGHT Fig. P8.17 ASSEMBLY Statics —— 297 8.18 A hot air balloon, shown in Fig. P8.18, is moored to the ground with three cables that are anchored at points A, B and C. The coordinates z (x, y, z) of the anchor points on the ground and on the basket are given in Fig. P8.l8. Determine the force exerted by each of the cables if the upward lift of the balloon is 750 lb. Assume that wind forces are negligible. - (o, o, 60) ft B (-25, - 15. 0)ft Fig. P8.18 A (25, —15, 0) ft C (15, 20, 0)ft 8.19 A circus cage, displayed in a large high ceiling auditorium, is supported above ground level by r the three wires, as illustrated in Fig. P8. 19. Determine the gage of the stainless steel wire required to support the cage weighing 2,100 lb if a safety factor of 3.25 is specified. The wire is fabricated from 4340 HR steel. The geometric parameters defining the assembly are listed in the table below. Points A, B and D locate the anchors for the cables. 4ft Fig. P8.l9 8.20 A local firm has constructed a small crane consisting of a boom supported by two steel 6“ wires BC and DE, as shown in Fig. P820. The boom is fixed to the supporting wall with a ball and socket joint at point A. The wires are anchored into the wall at points C and E. Each wire has a diameter of 0.250 in. and an ultimate tensile strength of 125 ksi. Determine the maximum weight that can be supported by the boom, the support reactions at point A and the forces in wires BC and DE. Fig. P820 Vac 298 —- Chapter 8 Space Structures and 3-D Equlibrium 8.21 A hand operated lifting mechanism called a windless utilizes a crank to rotate a drum, as shown in Fig. P821. The shaft of the z mechanism is supported by a wall mounted ball and socket joint at point A and a smooth journal bearing at point B. The arm and handle of the crank in the position shown is in the y-z plane. x For this position of the crank handle, determine the force F required to hold a weight of 50 kN in equilibrium. Also determine the reactions at the ball and socket joint and the journal bearing. DIA. D = 0.25 m Fig. P821 8.22 Repeat Problem 8.21, if the crank is rotated clockwise 90 degrees so that the arm and handle of the crank is in the x-y plane and the force F is acting in the positive z direction. For this position of the crank handle, determine the force F required to hold the weight of 50 kN in equilibrium. Also determine the reactions at the ball and socket joint and the journal bearing. 8.23 Repeat Problem 8.21, if the crank is rotated clockwise 180 degrees so that the handle of the crank is in the y-z plane and the force F is acting in the negative x direction. For this position of the crank handle determine, the force F required to hold the weight of 50 kN in equilibrium. Also determine the reactions at the ball and socket joint and the journal bearing. A cross-like base and a short pole, as shown in Fig. P824, support a tabletop with a uniform thickness. Determine the largest weight W that 0 75 m 0 75 can be applied to the table if it is placed at points A, B or C. The tabletop weighs 160 N/mz. The dimensions of the tabletop and the base are given in Fig. P824. ...
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