The beam is supported by double-shear pins at A, B, and C. The radius of all the pins are r = 8 mm. Hint: 1. Remember that rod BC is a 2-force member 0₁ d₁ B F₁ d2 F₂ Ö F₁ dz d₁ A
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- Determine the effective length factor (K) for all columns in the figure below: W16 X 57 W16 X 57 I F W16 X 57 W16 X 57 W16 X 57 B W21 X 93 E W21 X 93 H W21 X 93 J Hlage W16 X 57 W16 X 57 W16 X 57 A L4 X 4 X 3/4 D G Hinge 20 ft. 15 ft. 15 ft. 8 ft. 8 ft.s after the decimal po 200mm b18010 300mm L2 Joint D b18010 L1 "p double AR shear b180106003-1892615 B 50mm b18010 - 30mm b180106003-18926151 A frame is given above and an external load R is applied at point C. Pin connection Joint B b18010 b180106003- 18926151126 dg b1801000s Calculate the maximum normal stress for member BD by taking into account the reduced sectional areas at the pin connections. b180106003- 18926151126 (dD= 8mm, single shear b18010 b180108003-18926151126 at Dis in double shear, B is in single shear. b180106003-18926151126 b180106003 151126 24,05 MPa A b18010 18926151126 31,37 MPa b180106003 -18926151126 18926151126 01000s-18926151126 37,04 MPa b180108003-18926151126 b18010 828 18926151126 43,73 MPa bi8010 b180108003- 18928151126 b180106003-18926151126 18926151126 b180106003- 18926151126 b180100003-18926151126 b180106003- 18926151126 b180100003-18926151126 b18010 b180108003-18926151126 b180108003-18926151126 b18010s): The butt connection shown below is fastened by 20-mm diameter bolts. Find the maximum allowable load (P) that can be applied if the bearing stress, tensile stress and shearing stress is limited to 160 MPa, 80 MPa and 50 MPa, respectively. Use safety factor 1.5. P4- P4- 16 mm 50 100 50 50 100 50 40 80 40 12 mm P
- We will use both shearing and bearing analysis to determine the quantities of rivets needed to fasten BC and BE. We can determine two values then choose what will be more safe. ■ For Member BC: ■ Based on Shearing: V T == ■ Av Based on Bearing: P Ab 70MPa = 96000 N .n. (19) ²x n 1/4. π n = 4.84 5 rivets 96000 N (19mm) (6mm) xn 140MPa n = 46.015≈ 7 rivets For member BC, we must use 7 rivets since we must need a minimum of 7 rivets to resist bearing stress produced by the connection. If we only use 5 rivets, then the bearing stress will become 168.42 MPa. It will result to failure since the allowable bearing stress is only 140 Mpa. ■ For member BE: (Practice at Home) Pac EXAMPLE: 5. The figure shows a roof truss and the detail of the riveted connection at joint B. Using allowable stresses of t = 70 MPa and ob= 140 MPa, how many 19-mm diameter rivets are required to fasten member BC to the gusset plate? Member BE? What is the largest average tensile or compressive stress in BC and BE? Say…3. The aluminum block has the rectangular cross-section and is subjected to an axial compressive force of 8 kips. The 1.5-in side changed its length to 1.50014 inches. Use E = 10 x 10³ ksi. Calculate the new length of the 2-inch side. Answer: Lnew = 2.00019 in 1.5 in 2 in. 8 kip- 8 kip 3 in. 4. A solid cylinder of diameter D is subjected to an axial load P. Show that its change in diameter is 8D = 4Pv/лDE.A small stepladder has vertical rails and horizontal steps formed from a C-section aluminum channel. Two rivets, one in front and one in back, secure the ends of each step. The rivets attach the steps to the left and right hand rails. A 225 lb person stands in the center of a step. If rivets are formed of 6061-T6 aluminum, what should be the diameter d of the rivets? Use a factor of safety of 8 and round your answer to the nearest 1/16 of an in.
- 3. At temperature T₁, the two rigidly connected rods just fit the rigid supports. If both sections are identical except for the diameter, prove that the following equations are true when temperature rises to T₂. a. F= b. OAB C. OBC A x(T₂-T₁)лd²E 20 x(T₂-T₁)E 5 9x(T₂-T₁)E 5 -1/2- d B 1/12- d CA prestressed hollow box cross section is shown in the figure. The area of prestressed reinforcement in the tension zone is 1148 mm2. Use grade 270 for seven wire-strand tendons. fpy = specified yield strength of tendons fpu = specified tensile strength o pre stressing tendons fse = effective prestress after losses fse = 1022 MPa Aps = 1148 mm2 fpy = 0.95fpu fc’ = 34.5 MPa fpu = 1860 MPa a. Compute the Yp factor. b. Compute the stress in prestressed reinforcement at nominal strength. c. Compute for the design moment capacity. d. Compute the effective pre stressing force after losses of stress e. Compute the depth of the compression block. f. Compute the pre stressing steel ratio.A tie-down on the deck of a sailboat consists of a bent bar boiled at both ends, as shown in the figure. The diameter dBof the bar is 1/4 in., the diameter D Wof the washers is 7/8 in., and the thickness is of the fiberglass deck is 3/8 in. If the allowable shear stress in the fiberglass is 300 psi, and the allowable bearing pressure between the washer and the fiberglass is 550 psi, what is the allowable load P allowon the tie-down?
- Three round, copper alloy bars having the same length L but different shapes are shown, in the figure. The first bar has a diameter d over its entire length, the second has a diameter d over one-fifth of its length, and the third has a diameter d over one-fifteenth of its length. Elsewhere, the second and third bars have a diameter Id. All three bars are subjected to the same axial load P. Use the following numerical data: P = 1400 kN, L = 5m,d= 80 mm, E= 110 GPa. and v = 0.33. (a) Find the change in length of each bar. (b) Find the change in volume of each bar.80mm F 30mm 40mm 30mm d=15mm The steel plate shown is connected to the bracket by a 15mm bolt is subjected to tensile force F=70KN. Find out the average normal stress (N/mm2) at the plate. Select one: oa 281 Ob158 Oc 219 Dd18715 kN 2) Two objects are glued on the angled plane as shown in figure. If the ultimate stress for the glued joint are 20 MPa and 10 MPa for tension and shearing stress respectively, find the value of 0 that corresponds to the maximum factor of safety and find the value of this maximum factor of safety. 0.035 m 0.05 m