A composite section having an effective width of flangé of 2100 mm and a slab thickness of 150 mm is shown in the figure. The steel beam is a W 530 x 101 of A 36 steel with Fy = 250 MPa. Concrete fe = 20.7 MPa. Modular ratio n = 9. Assume full shoring and full composite action. 2100 mm Properties of W 530 x 101 A = 12900 mm2 150 mm d = 537 mm W= 101.4 kg/m k= 617 x 10 mm4 W 530 x 101
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a. Determine the moment of Inertia at the neutral axis.
b. Determine the resisting moment for the cross section shown.
c. Determine the stress of steel after concrete hardens.
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- A rectangular reinforced concrete beam has a length of 7.5 m. It is supported with a hinged at one end and a roller 2m from the other end. The width of beam is 350 mm and the overall depth is 550 mm. The beam is reinforced with 5D25 tensionreinforcement and 2D25 compression reinforcement located at 60 mm from the outermostfiber of the beam. The concrete strength fc = 28 MPa and steel yield fy= 390 MPa. Determinethe following:a. Sketch the beam and its cross sectionb. Stress in the compression steel.c. Moment capacity of the beam.d. Factored uniform load throughout the entire span of the beam that could carry.A rectangular beam has a width of 260 mm and an overall depth of 470 mm. concrete cover is 60 mm from the centroid of bars. Concrete compressive strength f’c = 21 MPa. Steel yield strength fy = 415 MPa for longitudinal bars and 275 MPa for hoops. Determine the shear strength (in N) provided by concrete using the simplified calculation (a) if the beam is subjected to shear and flexure only. _______ (b) if the beam is subjected to axial compression force of 80 KN. ________A composite floor system consists of steel beams supporting a formed steel deck and concrete slab. The deck is shown in Figure P, and the total depth from bottom of deck to top of slab is 61⁄2 inches. Lightweight concrete is used (unit weight =115 pcf), and the 28-day compressive strength is 4 ksi. The deck and slab combination weighs 53 psf. The beams are spaced at 12 feet, and the span length is 40 feet. There is a 20psf construction load, a partition load of 20 psf, other dead load of 10 psf, and a live load of 160 psf. The maximum permissible live-load deflection is Ly/360. Use the composite beam tables and select a W-shape with Fy= 50 ksi. Design the stud anchors. Use partial composite action and a lowerbound moment of inertia. a. Use LRFD. b. Use ASD
- A singly reinforced rectangular beam has a dimension b 310 mm and d = 410 mm Factored moment is equal to 100 kN-m, Concrete compressive strength is 24 MPa, Steel yield strength is 275 MPa and the reduction factor is 0.9. Determine the required steel area in mm?A rectangular beam has dimensions of 290 mm by 710 mm with an effective depth of 652 mm and is reinforced with 3- 20 mm ø. Concrete cover is 58 mm. The concrete cylinder strength f’c = 30.8 MPa and the tensile strength in bending is the modulus of rupture. The yield point of the steel is 414.2 MPa. The beam carries a bending moment of 66 kN-m. Use transformed section method to answer the following: (1) Compute the concrete compression stress at the top, (2) Compute the concrete tension stress at the bottom, (3) Compute the stress in the steel. (4) Assess the adequacy of the beam design.A rectangular concrete beam has a width of 400 mm and an effective depth of 700 mm. It is reinforced with five 28-mm diameter bars for tension only. Concrete strength is f's = 21 MPa and steel yield strength is fy = 275 MPa. Which of the following most nearly gives the distance of the neutral axis from the extreme compression concrete? A. 139.51 mm B. 151.93 mm C. 118.58 mm D. 188.15 mm
- A T beam has a concrete and steel strengths of 28 MPa and 420 MPa. The live load is 3830 Pa. while the dead load in addition to concrete's weight is to be 4097. The density of concrete is 2400 kg/m³. The slab is 125 mm thick while the effective depth is 600 mm, the total height of T-beam of 675 mm and the bottom width of T beam is 375 mm. The length of the beam is 7 meters. The center-to-center spacing of beams is 330 cm. Determine the arrangement of main reinforcement bars. Check for clear spacing.A rectangular beam 250 mm wide, 500 mm deep is reinforced at thebottom with 4-20-mm-diameter bars and at the top with 2-16-mmbars. Concrete cover to bar centroid at the top is 80 mm and at thebottom is 70 mm. Use concrete strength f’c = 21 MPa and steel yieldstrength fy = 415 MPa for 20-mm bars and fy = 275 MPa for 16-mm bars. 1. Determine the limiting tensile steel ratio for a tension controlledcondition in positive or negative bending with the given materialstrengths. ρt = [r] in 5 decimal places (ex. 0.00001)Question 1 A rectangular beam 250 mm wide, 500 mm deep is reinforced at the bottom with 4-20-mm-diameter bars and at the top with 2-16-mm bars. Concrete cover to bar centroid at the top is 80 mm and at the bottom is 70 mm. Use concrete strength f’c = 21 MPa and steel yield strength fy = 415 MPa for 20-mm bars and fy = 275 MPa for 16-mm bars. Determine the limiting tensile steel ratio for a tension controlled condition in positive or negative bending with the given material strengths. ρt = in 5 decimal places (ex. 0.00001) Determine the design moment capacity of the beam in positive bending. = kN∙m (whole number) Determine the design moment capacity of the beam in negative bending. = kN∙m (whole number)
- A floor systtem consist of a 75 mm concrete slab supported by continuous T beams with a span of 4.3 m spaced at 3 m on center. The beams have a web width, bw and effective depth, d. Calculate the necessary reinforcement for a typical interior beam if the applied factored load is 574 kN-m. Solve the following given a. ) bw = 400 mm; d = 500 mm; fy = 420 MPa; fc' = 28 MPa b. ) bw = 350 mm; d = 470 mm; fy = 420 MPa; fc' = 21 MPaA 6m simply supported beam has a width of 330 mm and an effectivedepth of 520 mm. The yield strength of steel is 280MPa and thecompressive of strength concrete is 26MPa. The compression steel, if necessary,should be reinforced at d’ = 80 mm. Determine the required area of steelreinforcement for the following factored moment:a. Mu = 90 kNm b. Mu = 430 kNm c. Mu = 850 kNm*Subject: Reinforced prestressed concrete - Civil Engineering *Please refer for my attached formula or guidelines solve this problem A one-way both ends continuous slab is to support the moments tabulated. Consider L=5m, Fc’=21MPa and fy = 415 MPA. Dead load Moments: +42kN.m at midspan ; -67 kN.m at support Live load Moment: +40kN.m at midspan, -44kN.m at support. Determine the minimum thickness of the slab.