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A reinforced concrete beam has a width of 300mm and an effective depth of 450mm. The beam is reinforced with 6-32mmØ bars at the bottom and 2-28mmØ bars at the top located 65mm from the maximum compression fiber. fc’ = 34.5 MPa, Fy = 345MPa. Assume that the contribution of the compression steel may not be neglected and that compression steel yields. 1) Which of the following gives the balanced steel ratio. 2) Which of the following gives the depth of the compression block. 3) Which of the following gives the nominal moment capacity of the beam. Solution: A composite beam is made up of a wide flange with two cover plates of 320mm x 12mm placed at the top and at the bottom. The beam has a simple span of 6m. and carries a total load of 360 kN/m. Allowable bending stress Fb = 150 MPa Allowable shear stress Fv = 100 MPa Allowable deflection δ = L/360 Prop. of the wide flange section. A = 0.02 m2 tw = 0.018 m. d = 0.56 m. I =0.001568 m4. E = 200,000 MPa. 1) Which of the following gives the section modulus of the section. 2) Which of the following gives the deflection of the beam. 3) Is the beam a. Adequate b. In adequate for flexure and shear c. In adequate for flexure and deflection d. In adequate for flexure, shear and deflection. Solution: A 590mm x 590mm reinforced concrete column with section shown is subjected to a service axial dead load of 450kN. Live load of 500kN, dead load moment of 135 kN/m and live load moment of 150 kN/m. fc’ = 21Mpa and fy = 415Mpa 1) Which of the following gives the equivalent eccentricity of the load on the column. 2) Which of the following gives the minimum area of steel reinforcement. 3) Which of the following gives the minimum size of steel bars. Solution: A rectangular reinforce concrete beam has a width of 250mm, a total depth of 600mm, and an effective depth of 500mm. It is reinforced with 3-25mmØ. Fc’ = 28MPa and fy = 415MPa. The beam is carrying a slab 150mm thick, 5m. wide. The beam has a span of 6m. If the unit weight of concrete is 24kN/m 3. 1) Which of the following gives the unfactored dead load acting on the beam? 2) Which of the following gives the ultimate moment capacity of the beam? 3) Which of the following gives the unfactored live load that the beam could support? Solution: The base of the footing is 1.8m. below the ground surface. It has a surcharge of 4.8kPa on the ground surface. The thickness of the footing is 1.2m. Allowable bearing pressure of the soil is 280kPa. Weight of concrete is 24kN/m3 and soil is 18kN/m3. 1) Which of the following gives the effective bearing pressure of soil. 2) Which of the following gives the distance of the resultant force from the extreme face of the column in order to have a uniform distribution of pressure. 3) Which of the following gives the dimension of the footing. Solution: A simply supported steel beam carries a uniform concrete slab 200mm thick. It carries a ceiling load of 500 Pa and live load pressure equal to 2000Pa. The length of the beam is 6meters and is spaced at 2m. on centers. Unit weight of concrete is 24kN/m2. Allowable bending stress for steel beam is 0.66Fy. Modulus of elasticity is 200GPa. Fy = 248MPa. 1) Which of the following gives the uniform load pressure carried by the beam? 2) Which of the following gives the load carried by the beam in kN/m? 3) Which of the following gives the most economical section? Section Moment of Inertia Depth W 12 x 26 0.0000849 m4 0.310 m. W 12 x 19 0.0000541 m4 0.309 m. W 12 x 14 0.0000369 m4 0.302 m. Solution: Problem A strip of 640 m2 is sold from a triangular field whose sides are 96 m, 72 m, and 80 m. The strip is of uniform width h and has one of its sides parallel to the longest side of the field. Find the width of the strip. A. 7.1 m B. 8.1 m C. 8.7 m D. 7.7 m Solution From ΔABC (By cosine law:) 802=722+962–2(72)(96)cos =54 64 722=802+962–2(80)(96)cos =47 22 tan =ch c=htan54 64 c=0 7096h tan =ch c=htan47 22 c=0 9254h a=b–c–d a=96–0 7096h–0 9254h a=96–1 635h AABED=21(a+b)h 640=21[(96–1 635h)+96]h 1280=192h–1 635h2 1 635h2–192h+1280=0 h=110 34 and 7 09 A closed traverse ABCD has the following data: Line Length Bearing AB 122.00 N 30° E BC 149.00 N 60° E CD 241.00 S 10° E DA 159.00 N 70° W 1. Determine the corrected bearing of side BC using compass rule. A. N 59° 11’E B. N 59° 11’E C. N 60° 12’E D. N 60° 49’E 2. Determine the corrected bearing of side CD using the compass rule. A. 149.632 m B. 148.368 m C. 149.547 m D. 148.453 m 3. Determine the corrected length of side BC using the compass rule. A. 242.067 m B. 241.852 m C. 240.148 m D. 239.933 m Solution: Line Length Bearing Lat Dep AB 122.00 N 30° E 105.655 61.000 BC 149.00 N 60° E 74.500 129.038 CD 241.00 S 10° E -237.339 -41.849 DA 159.00 N 70° W 54.381 -149.411 Perimeter 671 Error -2.802 -1.223 Compass rule: The correction to be applied to the latitude (or departure) of any course is to the total absolute correction in latitude (or departure) as the length of the course is to the perimeter of the traverse. Side CL Corrected CD Corrected Corrected Corrected Bearing Latitude Departure Length AB 0.510 106.165 0.222 61.222 122.552 N 29°58’15° E BC 0.622 75.122 0.271 129.309 149.547 N 59°50’43° E CD 1.007 -236.332 0.439 -41.410 239.933 S 9°56’18° W DA 0.664 55.045 0.290 -149.121 158.957 N 59°44’21° E Concrete beam 8meters long and spaced 4m center-to-center are used to support a concrete slab 115 mm thick. The beams have effective depth of 650 mm measured from the slab surface, b w=300mm, and are reinforced for tension only with six 28-mm-diameter bars. The beams are to be analyzed as T-beams. Steel yield strength fy=350MPa and concrete strength fc=21MPa. 1. Which of the following most nearly give the width of slab effective as T-beam, in millimeters? A. 2000 B. 2140 C. 4000 D. 3250 2. Which of the following most nearly give the depth of compression block in millimeters? A. 36.2 B. 45.2 C. 56.3 D. 62.4 3. Which of the following most nearly give the nominal moment capacity of the beam in KiloNewton-Meter. A. 563 B. 784 C. 952 D. 817 Solution: Steel column 3.6m long and hinged at both ends is used to carry an axial load of 800kN. The column is subject to end moments about its strong axis (single curvature) with M1 = 90%M2. The frame is braced against joint translation and is not subjected to any transverse loading. F y =248MPa, E=200GPa. The properties of the section are as follows: A=0.013 m2 rb=94 mm Sx=0.00099 m2 K=1.0 1. Which of the following most nearly gives the computed (actual) axial stress of the column in MegaPascals. A. 57 B. 75 C. 62 D. 68 2. Which of the following most nearly gives the allowable axial compressive stress of the column in MegaPascals. A. 114 B. 120 C. 133 D. 148 3. From a separate calculation with Fb = 149MPa, which of the following most nearly gives the maximum moment that the column can carry, in KiloNewtonMeter. A. 85.6 B. 75.4 C. 71.4 D. 78.8 Solution: A 4-m single span beam having a cross-section of 300mm x 500 mm carries a uniformly distributed load throughout its span. The beam is 80% stress grade Apitong with allowable bending stress of 16.5 MegaPascals, allowable shearing stress of 1.73 MPa and modulus of elasticity of 7.31 GigaPascals. Allowable deflection is 1/240 of the span. 1. Which of the following most nearly gives the value of the uniform load without exceeding the allowable bending stress of the beam, in KiloNewton per Meter. A. 118 B. 103 C. 132 D. 124 2. Which of the following most nearly gives the value of the uniform load without exceeding the allowable shearing stress of the beam, in KiloNewton per Meter. A. 63 B. 54 C. 87 D. 75 3. Which of the following most nearly gives the value of the uniform load without exceeding the allowable deflection, in KiloNewton per Meter. A. 102 B. 98 C. 124 D. 114 Solution: A rectangular reinforced concrete beam has a width of 300mm and an effective depth of 450mm to tension bars. The beam is reinforced with six 32-mmdiameter tension bars and two 28-mm-diameter compression bars with centroid 65mm from extreme concrete fiber. Concrete strength f c=34.5MPa and steel strength fy=345MPa. Assume that the contribution of the compression steel cannot be neglected and that compression steel yields. 1. Which of the following most nearly gives the balanced steel ratio if the beam were singly reinforced: A0.044 B.0.033 C.0.055 D.0.022 2. Which of the following most nearly gives the balanced steel ratio for doubly reinforced considering the effect of the compression steel: A.0.048 B.0.059 C.0.062 D.0.053 3. Which of the following most nearly gives the ultimate moment capacity of the beam A.632 B.724 C.517 D. 571 Solution: in KiloNewton-Meter. The beam is 150mm wide and 300mm deep, The allowable bending stress on extreme fiber is 12MPa. If x=2.5m: 1. Which of the following gives the maximum moment that the beam can resist, in KiloNewton-meter. A. 24 B. 16 C. 18 D. 27 2. Which of the following gives maximum value of P, in KiloNewton? A. 12.5 B. 8.6 C. 9.5 D. 16.4 3. Which of the following gives maximum value of P, in KiloNewton? A. 27 B. 24 C. 16 D. 18 Solution: A spiral column 500-mm in diameter is reinforced with 8-28mm diameter bars as shown. The interaction diagram for the column is also given. 1. Which of the following most nearly gives the reinforcement ratio in percent. A. 0.025 B. 0.032 C. 0.016 D. 0.041 2. Which of the following most nearly gives the ratio of eccentricity to column dimension in the direction of bending. A. 0.40 B. 0.30 C. 0.25 D. 0.35 3. Which of the following most nearly gives the nominal load capacity of the column. A. 2800 B. 2600 C. 2700 D. 2500 Solution: Rectangular beams 300mm wide 600mm effective deep and 5.8m long are spaced 3m on centers. These beams are used to support a 90-mm thick concrete slab poured monolithically with the beam, thus the beams may be considered as Tbeams. The beams are reinforced for tension only with eight 28-mm diameter bars. Concrete strength fc = 27MPa and steel strength fy = 345 MPa. The provisions of the 1992 Structrural Code of the Philippines regarding T-Beams is given. 1. Which of the following most nearly gives the effective flange width according to the 1992 NSCP, in millimeters. A. 1450 B. 1740 C. 3000 D. 1250 2. Which of the following most nearly gives the depth of compression block measured from the top of the beam, in millimeters. A. 68 B. 72 C. 60 D. 51 3. Which of the following most nearly gives the nominal capacity of the beam in KiloNewton-Meter. A. 854 B. 976 C. 753 D. 1104 Solution: A bar metal 25mm in diameter is tested on a length of 250mm. in tension the following results were recorded: Load (kN) Extension (mm) 10.4 0.036 The Young Modulus E is nearly: Solution: 31.2 0.089 A strip of steel 1mm thick is bent into an arc of a circle of radius 1.0m E is equal to 200GPa. The maximum bending stress is: Solution: Two pieces of 75mm x 400mm Yacal members under tension are connected together by means of a lap splice with 9pcs of 25mm dia. Bolts as shown. The working stresses for 80% visually stress-graded unseasoned Yacal are as follows: From table TM-6 Bending and tension parallel to grain Compression parallel to grain Compression perpendicular to grain Shear parallel to grian -24.5 MPa -15.8 MPa -6.27 MPa -2.49 MPa 1) Which of the following gives the net area of a timber member? Consider hole diameter to be 2mm larger than the bolt diameter 2) Which of the following gives the safe value of P considering the net area of the timber member? 3) Which of the following gives the safe value of P considering the bearing of the bolts on the timber. Solution: The T-section shown is formed by joining two rectangular pieces of wood together. The beam is subjected to a maximum shearing force of 60kN. 1) Which of the following gives the moment of inertia at the neutral axis. 2) Which of the following gives the shearing stress at the neutral axis. 3) Which of the following gives the shearing stress at the junction between the two pieces of wood. Solution: Concrete beam 8meters long and spaced 4m center-to-center are used to support a concrete slab 115 mm thick. The beams have effective depth of 650 mm measured from the slab surface, b w=300mm, and are reinforced for tension only with six 28-mm-diameter bars. The beams are to be analyzed as T-beams. Steel yield strength fy=350MPa and concrete strength fc=21MPa. 1. Which of the following most nearly give the width of slab effective as T-beam, in millimeters? A. 2000 B. 2140 C. 4000 D. 3250 2. Which of the following most nearly give the depth of compression block in millimeters? A. 36.2 B. 45.2 C. 56.3 D. 62.4 3. Which of the following most nearly give the nominal moment capacity of the beam in KiloNewton-Meter. A. 563 B. 784 C. 952 D. 817 Solution: A wall footing is shown. The unit weight of soil above footing is 18 kN/m 3 and unit weight of concrete is 23.5 kN/m 3. Concrete strength fc = 21 MPa and steel yield strength is fy = 414 MPa. The allowable soil bearing capacity is 210 kPa. 1. Which of the following most nearly gives the effective soil bearing capacity at the bottom of the footing in KiloPascals. A. 172 B. 195 C. 186 D. 164 2. Which of the following most nearly gives the dimension (width) of the footing in meter? A. 2.5 B. 2.1 C. 3.2 D. 2.8 3. Which of the following most nearly gives the spacing of the 28-mm diameter main bars, in millimeters? A. 300 B. 250 C. 400 D. 350 Solution: A built up section is made up of 3 rectangular plates welded to form an H-beam. The overall depth is 400mm and is 13 meters long. The slenderness ratio L/r = 200. The max. load in tension is 1600 kN and a min. load in compression is 260kN. The member is to carry a load P = max load + ½ min. load. 1) Compute the required area of the section if allowable stress is 185MPa. 2) Compute the width of the flange if r = ¼ width of flange. 3) Compute the thickness of the plate. Solution: A rectangular beam has a width of 250mm and an effective depth of 400mm. The beam is reinforced at the top and bottom section with a steel covering of 75mm for the compression bars and has a simple span of 6m.. If carries a uniform live load of 36kN/m and a dead load of 15kN/m. If fc’=21MPa, fy = 276MPa. 1) Which of the following gives the ultimate uniform load? 2) Which of the following gives the nominal moment capacity of the beam at balanced condition? 3) Which of the following gives the total steel area in tension. Solution: