Determine shear and moment equations of the beam shown. Neglect horizontal reactions since there are no axial forces. Summarize the equations solved. Example: Section 1: V1: M1:
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Determine shear and moment equations of the beam shown. Neglect horizontal reactions since there are no axial forces. Summarize the equations solved.
Example:
Section 1:
V1:
M1:
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- A flooring system consists of parallel I-beam sections spaced at 3 m on centers with simple spans of 6m. The beam supports a 200mm thick slab that laterally supports the top of the beams. The flooring system is designed for a superimposed load of 1750 N/m^2 The properties of the I-beam sections are: d= 352mm, tw= 7mm bf=170 mm, tf= 10mm Ix= 0.00012m^4, W= 44.85 kg/m Fy- 248 MPa,E= 200,000 GPa 1. Calculate the plastic section of the steel section in mm^3 2. Calculate the nominal strength (kN.m) of an individual beam if it is laterally supported by the concrete slab. 3. Calculate the unfactored service dead load on an individual beam in kN/m 4. Calculate the maximum service live load (kPa) the beam can sustain under LRFD provisions using φb= 0.9 5. Calculate the maximum live load (kPa) the beam can sustain under ASD provisions using Ωb=1.67The simply supported beam consists of a W530 × 66 structural steel wide-flange shape [E = 200 GPa; I = 351 × 106 mm4]. Determine(a) the beam deflection at point A.(b) the beam deflection at point C.Assume P = 44 kN, w = 87 kN/m, LAB = 4.0 m, LBC = 4.0 m, LCD = 4.0 m, LDE = 2.0 m.Answer:vA = mmvC = mmA beam of length 10m is symmetrically placed on two supports 7m apart. The loading is 15 kN/m between the supports and 20kN at each end. What is the central deflection of the beam? E = 210GN/mZ; I = 200 x 10-6m4. 5.2 (A/B). Derive the expression for the maximum deflection of a simply supported beam of negligible weight carrying a point load at its mid-span position. The distance between the supports is L, the second moment of area of the cross-section is I and the modulus of elasticity of the beam material is E. The maximum deflection of such a simply supported beam of length 3 m is 4.3 mm when carrying a load of 200 kN at its mid-span position. What would be the deflection at the free end ofacantilever of the same material, length and cross-section if it carries a load of l00kN at a point 1.3m from the free end?
- A built-up section consisting of W 350 x 90 with two 12 – mm plates welded to form a box section as shown in figure. The section is used as a column 10 meters long. The column is fixed at both ends, and braced at mid height about the weak axis (Y-axis). Use Fy = 248 MPa. Properties of W350x90: bf=250mm tf=16.4mm d=350mm tw=9.5mm Ix=226x10^6 mm^4 Iy=44.54x10^6 mm^4 A=11,550 mm^2 a. Determine the effective slenderness ratio of the column with respect to lateral buckling about the x-axis. b. Determine the effective slenderness ratio of the column with respect to lateral buckling about the y-axis. c. Determine the axial load capacity of the column in kN.An rcc beam having width 300mm and 500mm effective depth is reinforced with 4 bars of 16mm diameter in tension zone. Determine 1) depth of actual neutral axis 2) depth of critical neutral axis3) ultimate moment of resistance. Use M30 and Fe 415.The solid 34 mm diameter steel [E = 200 GPa] shaft supports two belt pulleys. For the loading shown, determine: (a) the shaft deflection at pulley B. (b) the shaft deflection at pulley C. Assume P = 810 N, Q = 480 N, LAB = 260 mm, LBC = 400 mm
- A floor system is supported by WF A36 steel beams 7.7m long and spaced 3.8m on centers. The beams are simply supported at their ends and are laterally supported over the entire span. Assume compact section and neglect beam self-weight. The properties of the beam section are: d = 559 mm, tw = 47mm, bf = 299mm, tf = 57mm, k = 72mm, shape factor SF= 1.2, Sx= 8478x10^3. Use allowable deflection (1/360) of beam span. Calculate the ULTIMATE floor load in KPa that the beam can carry against SHEAR. Express your answer in 2 decimal placesA W530x92 supports a uniformly distributed load of 12 kN/m (including the weight of the beam) and equal concentrated load P at quarter points (L/4, L/2, and 3L/4). The compression flange is laterally supported at quarter points and at the ends. The beam is 12m simply supported. Using A36 steel, the beam has the following properties: d = 533 mm bf = 209 mm tf = 15.6 mm tw = 10.2 mm k = 32 mm ry = 44.9 mm Sx = 2070 x 10^3 mm^3 Zx = 2360 x 10^3 mm^3 Es = 200,000 MPa Ix = 552 x 10^6 MPa Find the maximum allowable load P so that it will not exceed its maximum allowable moment capacity. Use conservative assumption for Cb.Ans- 5121 Ksi
- 38 - In the plane truss system, the loading status of which is evident in the figure, the support reactions and all rod forces will be found. A is the fixed joint and B is the sliding joint. Single upload P = 35 kN, dimensions a = 1 m and bar numbers are given. Accordingly By = ? A) 35B) 99C) 140D) 49.5E) 70The simply supported beam consists of a W530 × 66 structural steel wide-flange shape [E = 200 GPa; I = 351 × 106 mm4]. Determine (a) the beam deflection at point A. (b) the beam deflection at point C. Assume P = 46 kN, w = 74 kN/m, LAB = 4.2 m, LBC = 4.2 m, LCD = 4.2 m, LDE = 2.1 m.Question:- A 7.5 meters long simply supported structural steel beam carries two concentrated loads P at every third points. Use A 572 Grade 65 steel with Fy=448.18 MPa. The beam is W310x23.8 section having the given properties. A=3040mm² d= 305mm tw= 5.6mm bf=101mm tf= 6.7 mm Ix= 43x10⁶ mm⁴ Iy=1.2x10⁶mm⁴ a) Calculate the allowable bending stress of the compression flange of beam 7.5 fully supported against lateral movement. b) Based from the previous question, calculate the value of concentrated load P that the beam could support safety.