Design of Concrete Structures Worked Examples.pdf

MINISTRY OF SCIENCE AND TECHNOLOGY DEPARTMENT OF TECHNICAL AND VOCATIONAL EDUCATION

Sample Questions & Worked Out Examples For

CE-04014 DESIGN OF CONCRETE STRUCTURES

B.Tech. (Year II)

Civil Engineering

Sample Questions For

CE-04014 DESIGN OF CONCRETE STRUCTURES

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YANGON TECHNOLOGICAL UNIVERSITY Department of Civil Engineering Sample Questions for

CE-04014 DESIGN OF CONCRETE STRUCTURES (PART-I)

Chapter 1- Bond, Anchorage and Development Length *1.1. Figure 1.1 shows the column reinforcement for a 16 in. diameter concrete column, with fy = 60,000 psi and f'c = 5000 psi. Analysis of the building frame indicates a required As =7.10 in2 in the lower column and 5.60 in2 in the upper column. Spiral reinforcement consists of a

3/

8

in. diameter rod at 2 in. pitch. Column

bars are to be spliced just above the construction joint at the floor level, as shown in the sketch. Calculate the minimum permitted length of splice.

FIGURE 1.1 *1.2. Figure1.2 shows a deep transfer girder that carries two heavy column loads at its outer ends from a high-rise concrete building. Ground-floor columns must be offset 8 ft as shown. The loading produces an essentially constant moment (neglect selfweight of girder) calling for a concrete section with b = 22 in. and d = 50 in., with

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main tensile reinforcement at the top of the girder comprised of twelve No. 11 bars in three layers of four bars each. The maximum available bar length is 60 ft, so tensile splices must be provided. Design and detail all splices, following ACI Code provisions. Splices will be staggered, with no more than four bars spliced at any section. Also, investigate the need for special anchorage at the outer ends of main reinforcement, and specify details of special anchorage if required. Material strengths are fy = 60,000psi and f'c = 5000 psi.

FIGURE 1.2 ** 1.3. The beam of Fig.1.3 is simply supported with a clear span of 24.75 ft and is to carry a distributed dead load of 0.54 kips/ft including its own weight, and live load of 1.08 kips/ft, unfactored, in service. The reinforcement consists of three No. 10 bars at 16 in. effective depth, one of which is to be discontinued where no longer needed. Material strengths specified are fy = 60,000psi and f'c =4000 psi. No. 3 stirrups are used with cover of 1.5 in. at spacing less than ACI Code maximum.(a) Calculate the point where the center bar can be discontinued.(b) Check to be sure that adequate embedded length is provided for continued and discontinued bars.(c) Check special requirements at the support, where Mu=0. (d) If No. 3 bars are used for lateral reinforcement, specify special reinforcing details in the vicinity where the No. 10 bar is cut off.

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FIGURE 1.3 ** 1.4. The short cantilever shown in Fig.1.4 carries a heavy concentrated load 6 in. from its outer end. Flexural analysis indicates that three No. 8 bars are required, suitably anchored in the supporting wall and extending to a point no closer than 2 in. from the free end. The bars will be fully stressed to fy at the fixed support. Investigate the need for hooks and lateral confinement steel at the right end of the member. Material strengths are fy = 60,000 psi and f'c = 4000 psi. If hooks and lateral steel are required, show details in a sketch.

FIGURE 1.4 **1.5. The continuous beam shown in Fig.1.5 has been designed to carry a service dead load of 2 kips/ft including self-weight, and service live load of 3 kips/ft. Flexural design has been based on ACI moment coefficients of 1/11 and 1/16 at the face of support and midspan respectively, resulting in a concrete section with b=14 in. and d = 22 in. Negative reinforcement at the support face is provided by four No. 10 bars, which will be cut off in pairs where no longer required by the ACI Code. Positive bars

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consist of four No. 8 bars, which will also be cut off in pairs. Specify the exact point of cutoff for all negative and positive steel. Specify also any supplementary web reinforcement that may be required. Check for satisfaction of ACI Code requirements at the point of inflection and suggest modifications of reinforcement if appropriate. Material strengths are fy = 60,000 psi and f'c = 4000 psi.

FIGURE 1.5

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Chapter 2-Serviceability * 2.1. A rectangular beam of width b = 12 in., effective depth d = 20.5 in., and total depth h = 23 in. spans 18.5 ft between simple supports. It will carry a computed dead load of 1.27 kips/ft including self-weight, plus a service live load of 2.44 kips/ft. Reinforcement consists of four No. 8 bars in one row. Material strengths are fy = 60,000 psi and f'c = 4000 psi.(a) Compute the stress in the steel at full service load, and using the Gergely-Lutz equation estimate the maximum width of crack. (b) Assuming exterior exposure to moist air, confirm the suitability of the proposed design. * 2.2. For the beam of Prob. 2.1: (a) Compute the ACI z value using fs = 0.60fy as permitted by the ACI Code.(b) Compare against ACI Code limitations to determine if the design is satisfactory with respect to cracking. (c) Compare with indication of Table A.8 in App. A. **2.3. For the beam of Prob. 2.1: (a) Calculate the increment of deflection resulting from the first application of the short-term live load. (b) Find the creep portion of the sustained load deflection plus the immediate deflection due to live load. (c) Compare your results with the limitations imposed by the ACI Code, as summarized in Table 2.3. Assume that the beam is a part of a floor system and supports cinder block partitions susceptible to cracking if deflections are excessive. **2.4. A beam having b = 12 in., d = 21.5 in., and h = 24 in. is reinforced with three No. 11 bars. Material strengths are fy = 60,000 psi and f'c = 4000 psi. It is used on a 28 ft simple span to carry a total service load of 2130 lb/ft. For this member, the sustained loads include self-weight of the beam plus additional superimposed dead load of 510 lb/ft, plus 400 lb/ft representing that part of the live load that acts more or less continuously, such as furniture, equipment, and time-average occupancy load. The remaining 1220 lb/ft live load consists of short-duration loads, such as the brief peak load in the corridors of an office building at the end of a working day. (a) Find the increment of deflection under sustained loads due to creep. (b) Find the additional deflection increment due to the intermittent part of the live load. In your calculations, you may assume that the peak load is applied almost immediately after the building is placed in service, then reapplied intermittently. Compare with ACI Code limits from Table 2.3. Assume that, for this long-span floor beam, construction details are provided that will avoid damage to supported elements due to defections. If ACI Code limitations are not met, what changes would you recommend to improve the design?

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*** 2.5. A reinforced concrete beam is continuous over two equal 22 ft spans, simply supported at the two exterior supports, and fully continuous at the interior support. Concrete cross-section dimensions are b = 10 in., h = 22 in., and d = 19.5 in. for both positive and negative bending regions. Positive reinforcement in each span consists of one No. 10 bar and one No. 8 bar, and negative reinforcement at the interior support is made up of three No. 10 bars. No compression steel is used. Material strengths are fy = 60,000 psi and f'c = 5000 psi. The beam will carry a service live load, applied early in the life of the member, of 1800 lb/ft distributed uniformly over both spans; 20 percent of this load will be sustained more or less permanently, while the rest is intermittent. The total service dead load is 1000 lb/ft including self-weight. Find: (a) the immediate deflection when shores are removed and the full dead load is applied, (b) the long-term deflection under sustained load, (c) the increment of deflection when the short-term part of the live load is applied. Compare with ACI Code deflection limits; piping and brittle conduits are carried that would be damaged by large deflections. Note that midspan deflection may be used as a close approximation of maximum deflection.

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Chapter 3- Analysis and design for Torsion ***3.1 The 28 ft span beam shown in Figure (a) and (b) carries a monolithic slab cantilevering 6ft past the beam centerline, as shown in the section. The resulting L beam supports of live load of 900 lb/ft along the beam centerline plus 50psf uniformly distributed over the upper slab surface. The effective depth to the flexural steel centroid is 21.5 in., and distance from the beam surfaces to the centroid of stirrup steel is 1.75 in. Material strength are f'c = 5000 psi, fy = 60000 psi. Design the torsional and shear reinforcement for the beam.

FIGURE 3.1 *** 3.2. Architectural and clearance requirements call for the use of a transfer girder, shown in Fig. 3.2, spanning 20 ft between supporting column faces. The girder must carry from above a concentrated column load of 20 kips at midspan, applied with eccentricity 2 ft from the girder centerline. (Load factors are already included, as is an allowance for girder self-weight.) The member is to have dimensions b = 10in., h = 20in., xo = 6.5in., yo = 16.5 in., and d = 17 in. Supporting columns provide full torsional rigidity; flexural rigidity at the ends of the span can be assumed to develop 40 percent of the maximum moment that would be obtained if the girder were simply supported. Design both transverse and longitudinal steel for the beam. Material strengths are f'c = 5,000 psi and fy = 60,000psi.

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FIGURE 3.2 *** 3.3. The beam shown in cross section in Fig. 3.3 is a typical interior member of a continuous building frame, with span 30 ft between support faces. At factored loads it will carry a uniformly distributed vertical load of 3500 lb/ft, acting simultaneously with a uniformly distributed torsion of 3000 ft-lb/ft. Transverse reinforcement for shear and torsion will consist of No. 4 stirrup-ties, as shown, with 1.5 in. clear to all concrete faces. The effective depth to flexural steel is taken equal to 22.5 in. for both negative and positive bending regions. Design the transverse reinforcement for shear and torsion, and calculate the longitudinal steel to be added to the flexural requirements to provide for torsion. Torsional reinforcement will be provided only in the web, not in the flanges. Material strengths are f'c = 4,000 psi and fy = 60000 psi.

FIGURE 3.3

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Chapter 4- Short Columns * 4.1 For 14 × 22 rectangular column section is subjected to axial load and bending moment causing bending about the strong axis. It is reinforced parallel to the bending axis with As= A's = 4 No. 9 bars and d' =2.5 in. Material strengths are f'c = 4000 psi and fy = 60,000 psi. Bending will be about the strong axis. Using strain compatibility equations determine the load capacity Pn, moment capacity Mn when the eccentricity e = 20in. Use eb = 15in. Do not use ACI column interaction diagram charts. *4.2 For prob.4.2 using strain compatibility equations determine the load capacity Pn, moment capacity Mn when the eccentricity e = 10 in. Use eb = 15 in. Do not use ACI column interaction diagram charts. *4.3 The 12 × 20 column with reinforced eight No.9 bars arranged arround the column perimeter, with Pu = 275 kips, ex = 2.5 in., ey = 5.5 in., f'c = 4000 psi, fy = 60000 psi. Check the adequacy of the trial design (a) using reciprocal load method and (b) using load counter method. Use α = 1.15. * 4.4 Determine load Pb, moment Mb for 16 in. diameter circular spiral column reinforced with eight No.9 bars, cover to centroid of main bar = 2.5 in., cover to outer edge of ties (i.e. clear cover) = 1.5 in., with f'c = 4000 psi, fy = 60000 psi. Use large steel ratio. ** 4.5. The 20 × 20 square column shown in Fig.4.5 is subjected to axial load and bending moment causing bending about an axis parallel to that of the rows of bars. As = A's = 8.0 in2. What moment would cause the column to fail if the axial load applied simultaneously was Pn = 500 kips? Material strengths are f'c = 4000 psi and fy = 60 ksi. What is the strength Mn if it were loaded in pure bending (axial force = 0) about one principal axis?

FIGURE 4.5

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** 4.6. A short rectangular reinforced concrete column shown in Fig.4.6 is to be a part of a long-span rigid frame and will be subjected to high bending moments combined with relatively low axial loads, causing bending about the strong axis. Because of the high eccentricity, steel is placed unsymmetrically as shown, with three No. 14 bars near the tension face and two No. 11 bars near the compression face. Material strengths are f'c = 6 ksi and fy= 60 ksi. Calculate Pn, Mn , φPn , φMn.

FIGURE 4.6

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Chapter 5-Edge supported Slabs *5.1. A parking garage is to be designed using a two-way slab supported by16 x 26 in. monolithic beams on the column lines, as shown in Fig.5.1. Live loading of 100 psf is specified. Find the required slab thickness, using a steel ratio of approximately 0.005 maximum, and design the reinforcement for edge panel B and interior panel C. Detail the reinforcement, showing size, spacing, and length of rebars. All straight bars will be used. Material strengths will be fy = 60,000 psi and f'c = 4000 psi.

FIGURE 5.1

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**5.2. A footbridge is to be built, consisting of a one-way solid slab spanning 16 ft between masonry abutments, as shown in Fig.5.2. A service live load of 100 psf must be carried. In addition, a 2000 lb concentrated load, assumed to be uniformly distributed across the bridge width, may act at any location on the span. A 2 in. asphalt wearing surface will be used, weighing 20 psf. Precast concrete curbs are attached so as to be nonstructural. Prepare a design for the slab, using material strengths fy = 60,000psiand f'c = 4000 psi, and summarize your results in the form of a sketch showing all concrete dimensions and reinforcement.

FIGURE 5.2 ** 5.3. A reinforced concrete building floor system consists of a continuous one-way slab built monolithically with its supporting beams, as shown in cross section in Fig.5.3. Service live load will be 125 psf. Dead loads include a 10 psf allowance for nonstructural lightweight concrete floor fill and surface, and a 10 psf allowance for suspended loads, the self-weight of the floor. Using ACI coefficients, calculate the design moments and shears and design the slab, using a maximum tensile steel ratio of 0.006. Use all straight bar reinforcement. One-half of the positive moment bars will be discontinued where no longer required; the other half will be continued into the supporting beams as specified by the ACI Code. All negative steel will be discontinued at the same distance from the support face in each case. Summarize your design with a sketch showing concrete dimensions, and size, spacing, and cutoff points for all rebars. Material strengths are fy = 60,000 psi and f'c = 3000 psi.

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FIGURE 5.3 ** 5.4. For the one-way slab floor of Prob.5.3, calculate the immediate and long-term deflection due to dead loads. Assume that all dead loads are applied when the construction shoring is removed. Also determine the deflection due to application of the full service live load. Assuming that sensitive equipment will be installed 6 months after the shoring is removed, calculate the relevant deflection components and compare the total with maximum values recommended in the ACI Code. ** 5.5. A two-way concrete slab roof is to be designed to cover a transformer vault. The outside dimensions of the vault are 17 x 20 ft and supporting walls are 8 in. brick. A service live load of 80 psf distributed uniformly over the roof surface will be assumed, and a dead load allowance of 10 psf added to the self-weight of the slab. Design the roof as a two-way edge-supported slab, using f'c = 4000 psi and fy = 50,000 psi.

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YANGON TECHNOLOGICAL UNIVERSITY Department of Civil Engineering Sample Questions for CE- 04014 DESIGN OF CONCRETE STRUCTURES (PART-II) Chapter 1- Slender Columns **1.1 Figure shows an elevation view of multistory concrete frame building, with 48 in. wide × 12 in. deep beams on all column lines, carrying two-way slab floors and roof. The clear height of the column is 13ft. Interior columns are tentatively dimensioned at 18 × 18 in. and exterior columns at 16 × 16 in. The frame is effectively braced against sway by stair and elevator shafts having concrete walls that are monolithic with the floors, located in the building corners (not shown in figure). The structure will be subjected to vertical dead and live loads. Trial calculations by firstorder analysis indicate that the pattern of live loading shown in Fig.1.1, with full load distribution on roof and upper floors and checker board pattern adjacent to Column C3, produces maximum moments with single curvature in that column, at nearly maximum axial load. Dead loads on act all spans. Service load values of dead and live load axial force and moments for the typical interior column C3 are as follows: Dead load

Live load

P = 230 kips

P = 173 kips

M2= 2 ft-kips

M2 = 108 ft-kips

M1= -2 ft-kips

M1 = 100 ft-kips

The column is subjected to double curvature under dead load alone and single curvature under live load. Design column C3, using the ACI moment magnifier method. Use f'c = 4000 psi, fy = 60000psi.

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FIGURE1.1 ** 1.2. The structure shown in Fig.1.2a requires tall slender columns at the left side. It is fully braced by shear walls on the right. All columns are 16 and all beams are 24

×

×

16 in., as in Fig.1.2b,

18 in. with 6 in. monolithic floor slab, as in Fig.1.2c. Trial

calculations call for column reinforcement as shown. Alternate load analysis indicates the critical condition with column AB bent in single curvature, and service load thrust and moments as follows: from dead loads, P = 139 kips, Mtop = 61 ft-kips, Mbot = 41 ft-kips; from live load, P =93 kips, Mtop = 41 ft-kips, Mbot= 27 ft-kips. Material strengths are f'c = 4000 psi and fy = 60,000 psi. Is the proposed column, reinforced as shown, satisfactory for this load condition? Use Eq.(1.16) to calculate EI for the column.

FIGURE 1.2

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** 1.3. Refine the calculations of Problem1.2, using Eq.(1.15) to calculate EI for the column. Assume reinforcement will be approximately as given in Problem 1.2. ** 1.4. The first three floors of a multistory building are shown in Fig. 1.4. The lateral load resisting frame consists of 20 × 20 in. exterior columns, 24 × 24 in. interior columns, and 36 in. wide × 24 in. deep girders. The center-to-center column height is 16 ft. For the second story columns, the service gravity dead and live loads and the horizontal wind loads based on an elastic first-order analysis of the frame are: Cols. A2 and E2

Cols. B2 and D2

Col. C2

Pdead

348 kips

757 kips

688 kips

Plive

137 kips

307 kips

295 kips

Pwind

±19 kips

±9 kips

0 kips

Vwind

6.5 kips

13.5 kips

13.5 kips

M2,dead

31 ft-kips

M2,live

161 ft-kips

M2,wind

105 ft-kips

M1,dead

-34 ft-kips

M1,live M1,wind

108 ft-kips -98 ft-kips

A matrix analysis for the total unfactored wind shear of 53.5 kips, using values of E and I specified in Sec. 1.5, indicates that the relative lateral deflection of the second story is 0.24 in. Design columns B2 and D2 using Eq.(1.19) to calculate 8sMs. Material strengths are f'c = 4000 psi and fy = 60,000 psi.

FIGURE 1.4

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** 1.5 Repeat prob.1.5 using Eq.(1.20) to calculate δs Ms. Material strengths are f'c = 4000 psi, and fy = 60,000 psi.

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Chapter 2- Footings and Foundations * 2.1. A continuous strip footing is to be located concentrically under a 12 in. wall that delivers service loads D = 25,000 lb/ft and L = 15,000 lb/ft to the top of the footing. The bottom of the footing will be 4 ft below the final ground surface. The soil has a density of 120 pcf and allowable bearing capacity of 8000 psf Material strengths are f'c = 3000 psi and fy = 60,000 psi. Find (a) the required width of the footing, (b) the required effective and total depths, based on shear, and (c) the required flexural steel area. **2.2

A 12 × 18 in. column with f'c = 3000 psi, reinforced with six No.8 bars of

fy = 40000 psi, supports dead load of 100 kips and live load of 100 kips. The allowable soil pressure at bottom of the footing, which is 5 ft below grade, is 3 ksf. The surcharge load is 100 psf, f'c = 3000 psi., fy = 40000 psi. Design a rectangular footing whose side ratio is the same as that of the column section, the longer side of the footing being parallel to the longer side of the column. Assume average unit weight of the concrete and earth fill to be 125 pcf. Round up the theoretically compute values of width and length to next higher quarter-foot values. Try first with d =15 in. in the longer direction and 14 in. for punching shear checking. Check shear, moment, bearing and development length length. Find the total thickness using clear cover of 3 in. No.8, No.7 and No.5 bars are available. ** 2.3. An interior column for a tall concrete structure carries total service loads D = 500 kips and L = 514 kips. The column is 22 × 22 in. in cross section and is reinforced with twelve No. 11 bars centered 3 in. from the column faces (equal number of bars each face). For the column, f'c = 4000 psi and fy = 60,000 psi. The column will be supported on a square footing, with the bottom of the footing 6 ft below grade. Design the footing, determining all concrete dimensions and amount and placement of all reinforcement, including length and placement of dowel steel. No shear reinforcement is permitted. The allowable soil-bearing pressure is 8000 psf. Material strengths for the footing are f'c = 3000 psi and fy = 60,000 psi. ** 2.4. Two interior columns for a high-rise concrete structure are spaced 15 ft apart, and each carries service loads D = 500 kips and L = 514 kips. The columns are to be 22 in. square in cross section, and will each be reinforced with twelve No. 11 bars centered 3 in. from the column faces, with an equal number of bars at each face. For the column, f'c = 4000 psi and

fy = 60,000 psi. The columns will be supported on a

rectangular combined footing with a long-side dimension twice that of the short side.

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The allowable soil-bearing pressure is 8000 psf. The bottom of the footing will be 6 ft below grade. Design the footing for these columns, using f'c= 3000 psi and fy = 60,000 psi. Specify all reinforcement, including length and placement of footing, bars and dowel steel.

Worked Out Examples For

CE-04014 DESIGN OF CONCRETE STRUCTURES

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YANGON TECHNOLOGICAL UNIVERSITY Department of Civil Engineering Worked out Examples CE04014-DESIGN OF CONCRETE STRUCTURES

*1. ( 2,7 ). A rectangular beam of width b = 12 in., effective depth d = 20.5 in., and total depth h = 23 in. spans 18.5 ft between simple supports. It will carry a computed dead load of 1.27 kips/ft including self-weight, plus a service live load of 2.44 kips/ft. Reinforcement consists of four No. 8 bars in one row. Material strengths are fy = 60,000 psi and f'c = 4000 psi.(a) Compute the stress in the steel at full service load, and using the Gergely-Lutz equation estimate the maximum width of crack. (b) Assuming exterior exposure to moist air, confirm the suitability of the proposed design. Solution: Using Gergerly - Lutz Eqn: w = 1.27 + 2.44 = 3.71 k/ft M=

3.71× 18.52 = 1904.62 k-in 8

As = 4 N0.8 = 3.14 in2, dc = 2.5 in. ρ=

3.14 = 0.0128 12 × 20.5

Ec = 57000 n=

4000 = 3.605 × 106 psi

Es 29 × 10 6 = 8.04 ⇒ 8.0 = Ec 3.605 × 10 6

from table A-7, j = 0.879 fs =

1904.62 M = 33.66 ksi < fy = 60 ksi = As j d 3.14 × 0.879 × 20.5

effective conc. area = 12× 2.5 × 2 = 60 in2. A=

60 = 15 in2. 4

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w = 0.075 β fs

3

dc A

= 0.076 × 1.2 × 33.66 ×

3

2.5 × 15

= 10.27 thousand in. = 0.0103 in.

z = fs

3

d c A = 112.66 < 145

for exteroir exposure.