Q1-1
CIVIL ENGINEERING PRACTICE PROBLEMS
REINFORCED CONCRETE DESIGN CLOSED NOTES, HANDOUTS, BOOKS AND HOMEWORKS *Read problems completely and carefully before beginning to solve. Name:_______________________________________ Name:______________________________________ _ School ID No.:_______________ Section: _________________ I. Multiple Choice ( 1.5 points each) Instruction: Solved the following problems and write the corresponding letter of your answer on the space provided in the separate answer sheet provided. If your answer is not on the choices choose the nearest among the choices. USE CAPITAL LETTERS. Use NSCP 2010 otherwise stated.
75
A prestressed concrete beam 500 mm x 800 mm is simply supported over a span of L = 20 m. The tendons are placed 100 mm from the bottom of the beam. Initially the 2500 mm 2 tendons are tensioned up to a maximum pressure of 188.60 ksi after which the concrete is placed. After concrete hardens sufficiently, the tendons are cut there is a transfer of stress from tendons to concrete. The beam is then loaded by total dead load of 10 kN/m and live load of 15 kN/m. There is loss of stress at transfer of 10%. Use Working stress design. Determine the initial stress in the beam at the bottom fiber, in MPa. a. -23.77 b. -26.41 c. -8.13
d. -18.28
Calculate the total stress in the top fiber at L/3 from the e nds after the application of the loads, in MPa. a. -10.68 b. -10.16 c. –11.69 d. -9.14 Obtain the total stress in the bottom fiber at L/3 from the ends after the application of the loads, in MPa. a. -5.57 b. -20.83 c. -7.31 d. -2.93 The 6 m long prestressed cantilever beam shown in the figure RC-FE001 carries a concentrated live load of 18 kN at the free end and a uniform dead load due to its own weight. Unit weight of concrete is 24 kN/m 3. The prestressing steel is consists of 10 - 16 mm in diameter with total prestressing force applied at an eccentricity, “e” above the neutral axis of the gross-section. Use Working stress design. Use: Use: b = 400 mm; h = 600 mm; L = L = 6 m Determine the required prestressing pressure (in MPa) if the stress on top is -11 MPa and at the bottom is +3.5 MPa due to initial prestress. a. 548.92 b. 447.62 c. 583.10 d. 763.39 Determine the required prestressing pressure (in MPa) if the stress on top is -0.5 MPa and at the bottom is -12 MPa at the fixed end due to initial prestress and service loads. a. 746.04 b. 484.29 c. 366.45 d. 556.25 Determine the required prestressing force (in kN) if the stress on top is -0.5 MPa and in the bottom is -12 MPa at the fixed end due to initial prestress and service loads. a. 975 b. 740 c. 1,500 d. 1,120 A spiral column 500 mm in diameter, it is reinforced with 6 – 32 mm Ø bars and has an unsupported height of 3 m. The column is bent in single curvature and is braced against sidesway. Bending is about the x-axis x-axis (see figure RC-FE005). Compressive strength of concrete = 27.5 MPa (normal weight) Steel yield strength = 413 MPa Clear cover = 40 mm Spirals = 10 mm spaced at 50 mm O.C. Determine the ultimate concrete shear strength of the spiral column using NSCP 2010. Determine the depth in the axis of bending, in mm. a. 491 b. 400
c. 600
d. 468
Determine the nominal concrete shear strength along the x-axis, x-axis, in kN. a. 113.63 b. 116.84 c. 151.51
d. 155.79
Calculate the ultimate shear capacity of the column, in kN. a. 551.26 b. 461.90 c. 527.08
d. 463.27
CIVIL ENGINEERING FINAL EXAMINATION
Q8-2
The flooring of a warehouse is made up of double-tee joists (DT) as shown RC-FE003. The joists are simply supported on a span of 7.5 m and are pre-tensioned to a total initial force of 1,500 kN with one tendon in each stem, located at 75 mm above the bottom fiber, loss of stress at service load is 20%. Unit weight of c oncrete is 24 kN/m 3. Load imposed on the joists joists are: Dead Load = 2.3 kPa Properties of DT: A = 200, 000 mm 2;
Live load = 6 kPa I = 1880 x 106 mm4;
yt = 88 mm;
y b = 267 mm;
a = 2.4 m
Compute the stress at the top fibers at midspan due to the initial pre stressing force alone, in MPa. a. +5.98 b. +4.78 c. -48.40 d. -38.72 Compute the resulting stress at the top fibers of the DT at mid-span due to service loads and prestressing force, in MPa. a. -63.41 b. -23.72 c. -40.27 d. -14.04 What additional super imposed load can the DT carry such that the resulting stress at the top fibers at midspan is zero, in kPa? a. 10.18 b. 17.77 c. 4.24 d. 5.86 As shown in Figure RC-FE008 , beam DEF is reinforced as follows: Main reinforcements at supports: Main reinforcements at midspan: Top bars……………………………5 – 25 mm ɸ Top bars……………………………3 – 25 mm ɸ Bottom bars……………………..…3 – 25 mm ɸ Bottom bars….………….…………3 – 25 mm ɸ Stirrups………………………….…10 mm ɸ Material strength: Concrete: f c’ = 27.5 MPa Steel : f y = 415 MPa (main bars) f yv yv = 275 MPa (stirrups)
Dimensions: Beam (below slab): bw x h = h = 350 mm x mm x 350 350 mm Slab thickness: t f = = 100 mm Column section: 350 mm x mm x 350 350 mm Clear cover: 50 mm S1 = S2 = S3 = 2.6 m; S4 = S5 = 6.5 m Find the ultimate load W u (kN/m) which the beam DEF can support based on its flexural reinforcements at supports. Use steel cover of 70 mm. a. 83.01 b. 60.37 c. 75.47 d. 67.92
Find the factored moment capacity M u in kN.m of the beam DEF at midspan. Use steel cover of 70 mm. a. 285.44 b. 188.47 c. 194.93 d. 107.30 Find the shear (kN) at end E of span EF if W u = 60 kN/m. a. 212.18 b. 162.44
c. 194.93
d. 244.00
An isolated T beam is composed of a flange 550 mm wide and 150 mm deep cast monolithically with a web of 250 mm width that extends 600 mm below the bottom surface of the flange to produce a beam of 750 mm total depth. Tensile reinforcement consists of 4-32 mm ϕ bars placed in two horizontal rows separated by 25 mm clear spacing. The centroid of the bar group is 650 mm from the top of the beam. The concrete has a strength of 20.68 MPa, and the yield strength of the steel is 413.57 MPa. What is the design moment capacity of the beam? Which of the following gives the location of the neutral axis from the extreme tension fiber, in mm? a. 161.90 b. 144.42 c. 605.58 d. 588.10 Which of the following gives the actual strain of the tension bars, in MPa? a. 0.00207 b. 0.00785 c. 0.00795
d. 0.00904
Which of the following gives the nominal moment capacity of the beam, in kN.m? a. 695.24 b. 773.25 c. 864.80
d. 778.32
Q1-3
CIVIL ENGINEERING PRACTICE PROBLEMS
After frame analysis resulting bending moments at working loads of a beam are as follows: MDL = 110 kN.m MLL = 60 kN.m MEQ = 45 kN.m Given: Given: Concrete compressive strength: f c’ = 28 MPa Reinforcing steel yield strength: f y = 415 MPa Required strength: U = 1.2D + 1.0L + 1.0E Concrete cover to centroid of reinforcement r einforcement = 70 mm Using a beam 250 mm wide, find the required total beam depth (mm), if this beam is to be designed as singly reinforced. Use design steel ratio, ρ = ¼ (ρ max+ ρ b). a. 650 b. 550 c. 600 d. 500 Using a beam with dimension b x h = h = 300 mm x mm x 600 600 mm, calculate the minimum number of 20 mm Ø bars required. a. 4 b. 5 c. 6 d. 8 Using a beam with dimension b x h = h = 250 mm x mm x 500 500 mm reinforced with 3 - 25 mm Ø bars, find the resulting nominal bending strength M n (kN.m). a. 231 b. 208 c. 275 d. 237 The figure shown in RC-FE011 shows the shear force at the column section of a building with transverse confining reinforcement. Use: Use: b = 400 mm; h = 800 mm; d b = 28 mm Clear cover of 12 mm ϕ ties (PC) = 40 mm f c’ = = 28 MPa f y = 415 MPa (for main bars) f yh = 278 MPa (for tie bars) The NSCP specifies the transverse confining reinforcement in accordance with the code for seismic design. Determine the required spacing (in mm) of lateral reinforcement for a factored shear load V uy = 500 kN if the allowable concrete shearing stress is 0.88 MPa. a. 100 b. 170 c. 150 d. 90 What is the maximum spacing (in mm) of the 12 mm ϕ transverse reinforcement? a. 100
b. 150
c. 120
d. 90
Determine the required spacing (in mm) of the confining hoop reinforcement in accordance with the code for seismic design. a. 50
b. 160
c. 120
d. 70
A column shown in figure RC-FE010 is a T-section and has PVC pipes with outside diameters of 76 mm were embedded on it. Given Data: Longitudinal bars: bars: Lateral Ties: As1 = 6-20 mm Ø bars in compression 10 mm Ø bars with f yv yv = 275 MPa As2 = 4-32 mm Ø bars in tension Clear cover concrete cover ties = 40 mm f y= 415 MPa fc’ = 27.5 MPa Use: b1 = 600 mm; b2 = 300 mm; h1 = 250 mm; h2 = 350 mm Consider the concrete area displaced by the compression steel. Determine the location of the geometric centroid of t he section from y-axis, y-axis, in mm. a. 304.60 b. 278.23 c. 257.44
d. 290.85
Determine the location of the plastic centroid of the section from y-axis, y-axis, in mm. a. 289.48 b. 290.85 c. 304.60
d. 278.23
Calculate the percentage loss in strength of the column based on its axial capacity without embedment. a. 7.99 b. 46.69 c. 2.30 d. 8.69
CIVIL ENGINEERING FINAL EXAMINATION
Q8-4
Refer to figure RC-FE007 . Given : : f c’ = 27.6 MPa and f y = 413.6 MPa.
b1 = 125 mm; b2 = 650 mm; Bottom bars: bars: 4 – 36 mm ɸ bars
t = 125 mm;
Calculate the depth of compression block, in mm. a. 178.06 b. 93.83
h1 = 300 mm;
c. 22.06
Compute the ultimate moment capacity of the beam, in kN.m. a. 544 b. 641 c. 712
S = = 75 mm
d. 79.76 d. 408
Determine the safe service uniform live load in addition to its own weight, in kN/m. Assume that the beam is having a simple span of 8 m. a. 46.07 b. 80.06 c. 74.77 d. 42.73 Reinforced concrete tied columns are to support the fences of San Carlos Seminary located in Mabolo, Cebu City. The columns are typical having dimensions of 250 mm x 250 mm, height of 3 m and reinforced with 4 – 16 mm φ vertical bars. = 21 MPa; Weight of concrete = 23.54 kN/m 3 Given: f c’ = f y = 415 MPa Clear cover = 40 mm; main bar = 16 mm φ; lateral ties = 10 mm φ Calculate the ultimate axial capacity of the column at e = 0, in kN. a. 1,435.03 b. 932.77 c. 1,148.03
d. 746.22
After 40 years some columns lean at an angle of 15º from the vertical because of the unstable soil foundations. Calculate the actual nominal bending moment produced at the base, in kN.m. a. 3.16 b. 5.30 c. 1.71 d. 2.06 Determine the nominal moment capacity of the column, in kN.m. a. 50.45 b. 31.87 c. 36.05
d. 53.80
The figure shown in Fig. RC-FEQ008 is a floor framing plan of a reinforced concrete building. All beams are 300 mm x 600 mm. Slab thickness = 100 mm; Super imposed dead load = 3.6 kPa; Live load = 4.0 kPa 3 Concrete unit weight = 24 kN/m Columns at E and H are deleted thus girder BEHK alone supports beam DEF at E and beam GHI at H. Dimensions are: S1 = 2.5 m S2 = 2.5 m S3 = 2.5 m S4 = 6.0 m S5 = 6.0 m Calculate the uniformly distributed service dead load at beam DEF, in kN/m. a. 22.32 b. 26.04 c. 18.60 d. 17.00 Calculate the uniformly service live load at beam DEF, in kN/m. a. 17.00 b. 10.00 c. 16.00
d. 14.40
Calculate the total ultimate load (in kN) concentrated at E induced by beam DEF using the tributary area method. a. 115 b. 145 c. 86 d. 230 A rectangular concrete beam having a width of 450 mm has a total depth of 575 mm. It is reinforced for tension having a steel area of 3200 mm 2 and steel area for compression equal to 900 mm 2. The compression bars are placed at a distance of 62.5 mm from the top of the beam while tension bars are placed 75 mm from the bottom of the beam.
Given: f c’ = 21 MPa and f y = 345 MPa. Which of the following gives the location of the neutral axis from the extreme compression fiber, in mm? a. 122.84 b. 104.42 c. 137.44 d. 161.70 Which of the following gives the actual stress of the compression bars, in MPa? a. 345.0 b. 294.74 c. 1,842.11
d. 1,255.33
Q1-5
CIVIL ENGINEERING PRACTICE PROBLEMS
Which of the following gives the ultimate moment capacity of the beam, in kN.m? a. 491.63 b. 476.13 c. 442.57 The figure shown in Fig. RC-FE009 is a floor framing plan of a reinforced concrete building. bw x h (below the slab) = 300 mm x 350 mm; Slab thickness, t f = = 100 mm Super imposed dead load = 2.4 kPa Live load = 3.8 kPa Concrete: fc’=20.7 MPa Steel: fy= 414 MPa 3 Concrete unit weight = 24 kN/m Clear cover to stirrups = 50 mm Stirrups = 10 mm ɸ Column = 300 mm x 300 mm S1 = S2 = S3 = 3.0 m S4 = S5 = S6 = 8.0 m Compute the total ultimate load to design beam I-J-K-L, in kN/m. a. 37.10 b. 36.86 c. 41.81
d. 428.52
d. 28.32
If the design ultimate load, Wu = 45 kN/m, find the negative moment at the end of K of span JK, in kN.m. a. 266.81 b. 166.75 c. 242.55 d. 190.58 How many 25 mm ɸ bars are required at the end K of span KL if the design ultimate load, Wu = 50 kN/m? a. 6 b. 7 c. 8 d. 4 Refer to Fig. RC-FE014. Use ACI Moment Coefficient as shown on section 408.4. From the given floor floor plan, the following following data are obtained: obtained: Dimensions: Ultimate Load, W u = 20 kN/m Beam b x h x h = 300 mm x mm x 400 400 mm f y(main bar) = 275MPa Clear cover to slab reinforcement = 20 mm f y(temp. bar) = 275 MPa Slab reinforcement = 12 mm ϕ f c’ = 20.7 MPa Slab thickness = 90 mm S1 = S2 = 2.8 m; S3 = 6.0 m What is the spacing of reinforcement r einforcement (mm) required for the moment at the interior beam support BE? a. 210 b. 200 c. 150 d. 120 What is the spacing of reinforcement r einforcement (mm) required for the positive moment at the span bounded by BEFC? a. 150 b. 200 c. 170 d. 180 Determine the maximum spacing (mm) of the 12 mm ϕ bars. (Hint: Check for spacing for crack control .) control .) a. 250 b. 270 c. 300 d. 450 A deck of slab of the bridge in a section over intermediate supports as shown in RC-FE002 is prestressed to limit cracking and deflection. Unit weight of concrete is 24 kN/m 3. The total prestressing force is 45,500 kN. Assume that there is a loss of prestress of 15% at service loads where the uniform live load is 240 kN/m. Assuming intermediate supports are fixed and having uniform clear distances of 30 m. Use: Use: b f = 11.0 11.0 m; h = 2.75 m; t 1 = 250 mm; t 2 = 450 mm 4 2 I xx = 8.3 m ; A = A = 8.0 m ; e = 575 mm y = 1.025 m; Determine the stress on top fiber due to prestress, in MPa. a. -7.58 b. -8.92 c. -11.12 d. -9.46 Calculate the total stress in the bottom fiber at fixed end due to prestress and service loads, in MPa. a. -6.98 b. -4.21 c. -4.25 d. -6.95 Obtain the eccentricity in order that the total stress on the top fiber at the fixed will be -6 MPa, in mm. a. 593.70 b. 1,653.92 c. 505.39 d. 1,081.80 It is the point through which the resultant of the resistance to the applied lateral force acts. a. shear wall b. center of mass c. eccentricity d. center of rigidity A standard hook has a ___ degree bend plus 12d b (bar diameters) extension at the free end of bar. a. 180 b. 90 c. 45 d. 30
CIVIL ENGINEERING FINAL EXAMINATION
P L
Q8-6
a
Service loads yt
b
N.A.
e
d
yb
y3
L
Fig. RC-FE003
Fig. RC-FE001 b f
t 1 e
N.A.
x
h
t 2
x
y
PC
Fig. RC-FE002
d b
b
x d s
D
h
Fig. RC-FE005
Fig. RC-FE006 Fig. RC-FE007
t
h1
S S b1
b2 b
b1
h
x
CIVIL ENGINEERING FINAL EXAMINATION
V uy uy
Line 1
Q8-8
PC
d b
b
x
d s
h Fig. RC-FE011 D
A
t f As’
S1
B
E h’
S2
C
As
F S3
FRAMING PLAN
Fig. RC-FE014
bw BEAM SECTION
410.7.4 MAXIMUM SPACING FOR CRACK CONTROL
The spacing s spacing s of of reinforcement closest to a surface in tension shall not exceed that given by:
280 2.5cc f s
s 380
280 , where cc is the least distance from the surface of reinforcement or reinforcing steel to the f s
but not greater than 300
tension face. If there is only one bar or wire nearest to the extreme tension face, s used s used is the width of the extreme tension face. Calculated stress in reinforcement f s in MPa closest to the tension t ension face shall be computed based on the unfactored moment. It shall be permitted to take f s as 2/3 of specified yield strength f strength f y. 401.01.01 Effective span for simply supported and continuous beams are as follows:
1) Simply supported beams The effective span of a simply supported beam shall be taken as the smaller of the distance between the centers of bearing, or the clear distance between supports plus the effective depth.
Q1-9
CIVIL ENGINEERING PRACTICE PROBLEMS
2) Continuous beams If the width of support is less than 1/12 of the clear span, the effective span shall be taken a s stated (1) above. If the supports are wider than 1/12 of the clear span or 600 mm, whichever is less, the effective span shall be as follows: a) For end span with one fixed f ixed and the other continuous or for intermediate spans, the effective span shall be the clear s pan between supports. b) For end span with one end free and other continuous, the effective span shall be equal to the clear span s pan plus half the t he effective depth of the beam or the clear span plus half the width of the discontinuous support, whichever whichever is less. 3) Monolithic 3) Monolithic frames frames In case of monolithic frames, the effective span shall be equal to the distance between intersections of the center lines of the connecting members. 4) Cantilever beams The effective length of the cantilever shall be taken as its length to the face of the supports plus half its effective depth except where it forms the end of a continuous beam where the length to the center of the support shall be used. 408.4 Method of Analysis moments and shears shall to be used in design of 408.4.3 As an alternate to frame analysis, the following approximate moments continuous beams and one-way slabs ( slabs reinforced to resist flexural f lexural stresses in only one direction), provided: 1. There are two or more spans. 2. Spans are approximately equal, with the larger of two adjacent spans not greater than the shorter by more than 20 percent. 3. Loads are uniformly distributed. 4. Unfactored live load, L does not exceed three times Unfactored dead load, D. 5. Members are prismatic. For calculating negative moments, l n is taken as the average of the adjacent clear spans lengths.
End Spans Discontinuous end unrestrained………………… unrestrained………………………………………………………………….. ……………………………………………….. Discontinuous end integral with support…………………………………………… support………………………………………………………….. ……………..
wu l n 2
Interior Spans……………………………………………………………..……………………………..
11 wu l n 2 14 wu l n 2 16
At exterior face of first interior supports a) Two spans…………………...………………………………………………………………….. b) More than two spans……………….………………………………………………………….. spans……………….………………………………………………………….. c) At other faces of interior supports….…………………………………………………………..
wu l n 2
9 wu l n 2 10 wu l n 2 11
d) At face of all supports for: slabs with spans not exceeding 3 m ; and beams where ratio of sum of column stiffness to beam stiffness exceeds eight at each end of the span …………..………..
wu l n 2 12
CIVIL ENGINEERING FINAL EXAMINATION
Q8-10
At interior face of exterior support for members built integrally with supports: a) Where support is a spandrel beam……..……………………………………………………….. b) Where support is a column………….………………………………………………………….. column………….…………………………………………………………..
a) At face of first interior support..………………………………………………………………..
wu l n 2 24 wu l n 2 16
1.15wu l n
b) At face of all other supports………….………………………………………………………….. supports………….…………………………………………………………..
2 wu l n 2
Limits for compression reinforcement A) Minimum ratio of spiral reinforcement
a)
s
b) s
A f ' 0.45 g 1 c Ac f yh 0.12
Equation 410.10-1
f 'c
Equation 410.10-2
f yh
Note: whichever is bigger where: Ag = gross area of column Ach = core area to outside of spirals f yh yh = specified yield strength B) Minimum area of rectangular hoop reinforcement in (tied) column.
A g
f ' 1 c Ac f yh
a) A sh 0.3Shc
b) A sh
0.09Shc
f 'c
Equation 410.10-3
Equation 410.10-4
f yh
where: Ach = the cross sectional area of the column core, measured out to out of the transverse reinforcement S = spacing of transverse reinforcement r einforcement hc = cross-sectional dimension of the column core, measured center to center of the confining reinforcement f yh yh = specified yield strength of transverse reinforcement r einforcement (tied column). C) Maximum spacing of transverse reinforcement a) ¼ of minimum dimension b) 6db or 150 mm
350 h x 3
c) The distance, S o 100 where:
hx = maximum horizontal spacing between hoops or cross tie legs on all faces of the column, maximum value of 350 mm Note: So shall not less than than 100 mm nor more more than 150 mm
