## Prestressed Concrete Structures MCQ Set 1

1.Calculate ultimate moment and shear of effective span is 30m, live load is 9kn/m, dead load excluding self weight is 2kn/m, load factors for dead load is 1.4 for live load is 1.6 cube strength of concrete f_{cu} is 50n/mm^{2} cube strength at transfer is f_{ci} is 35n/mm^{2}, tensile strength of concrete E_{c} is 34kn/mm^{2} loss ratio ɳ is 0.85 and 8mm diameter high tensile strength f_{pu} is 1500n/mm^{2} are available for use and the modulus of elasticity of high tensile wires is 200kn/mm^{2}?

a) 340 and 450kn

b) 240 and 340kn

c) 140 and 240kn

d) 100 and 200kn

### View Answer

_{min}/W

_{ud }= (50x2400x9.81×0.125x25x30/50×10

^{6}x0.85

^{2}) = 0.31 Ultimate load excluding the factored selfweight = (1.4×2)+(1.6×9) = 17.2kn/m, W

_{ud}= 17.2/1-1.4×0.31) = 30KN/M, W

_{min}= (0.31×30) = 9.3kn/m, Ultimate moment , M

_{u}= (0.125x30x30

^{2}) = 3400knm, Ultimate shear, V

_{u }= (0.5x30x30) = 450kn.

2. Find cross-sectional dimensions thickness of web if h_{f}/d ratio is 0.23 and b_{w}/b ratio is 0.25 and b is 0.5d?

a) 100mm

b) 110mm

c) 120mm

d) 30mm

### View Answer

_{f}/d =0.23 and b

_{w}/b = 0.25 and b = 0.5d, M

_{u}= 0.10f

_{cu}bd

^{2}d = (3400×10

^{6}/0.10x50x0.5)

^{1/3}= 1130mm, h = (1130/0.85) = 1300, b = 600mm, h

_{f}= (0.2×1130) = 250mm, adopt an effective depth, d = 1150mm, thickness of web, b

_{w}= (0.6vu/fth) = (0.6x450x10

^{3}/1.7×1300) = 120mm.

3. Calculate working moment if design working load is 19.8kn/m covered over a span of 30m( actual self weight of girder is 8.8kn/m)?

a) 3000

b) 2000

c) 4340

d) 2230

### View Answer

_{min}= 990knm, Design working load = 19.8kn/m, Working moment M

_{d}= (0.125×19.8×30

^{2}) = 2230knm.

4. Find the Permissible stresses and range of stresses for class 1 structure f_{cu} = 50n/mm^{2},f_{ck} = 35n/mm^{2} according to BS: 8110 recommendations for f_{cu} = 50n/mm^{2} and f_{ci} = 35n/mm^{2},f_{ct} = 0.5f_{ci}= 17.5n/mm^{2}?

a) 16.5n/mm^{2}

b) 12.56n/mm^{2}

c) 13.56n/mm^{2}

d) 12.00n/mm^{2}

### View Answer

_{cu}= 50n/mm

^{2},f

_{ck}= 35n/mm

^{2}according to BS: 8110 recommendations for f

_{cu}= 50n/mm

^{2}and f

_{ci}= 35n/mm

^{2}, f

_{ct}= 0.5f

_{ci}= 17.5n/mm

^{2}For class 1 structure f

_{u}= h

_{tw}= 0, f

_{br}= (ɳf

_{ct}-ftw) = (0.85×17.5) = 15n/mm

^{2}, f

_{cw}= 0.33f

_{cu}= (0.33×50) = 16.5n/mm

^{2}, f

_{cu}= (fcw-ɳfu) = 16.5n/mm

^{2}.

5. Find prestressing force if area is 36.75mm^{2} of eccentricity 580given f_{inf} is 26.5kn/m and z_{b} is 99×10^{6}?

a) 405

b) 308

c) 453

d) 206

### View Answer

^{2}, e = 580, f

_{inf}= 26.5kn/m, z

_{b}= 99×10

^{6}p =(Af

_{inf}Z

_{b}/Z

_{b}+A

_{e}) =(367500×26.5x99x10

^{6}/(99×10

^{6})+(367500×580)) = 308x104kn/m

^{2}.

6. Find force in cable using Freyssinet cables 12-8mm diameter and stressed to 1100n/mm^{2} of eccentricity 50 and the prestressing force is given as 1000n/mm^{2}?

a) 660kn

b) 234kn

c) 300kn

d) 230kn

### View Answer

^{2}, e = 50, prestressing force =1000n/mm

^{2}Force in each cable = ( (12x50x1100)/1000)) = 660kn.

7. Find ratio for ultimate flexural strength at the centre – span section given that A_{ps} = 3000mm^{2}, d= 1150mm, f_{cu} = 50n/mm^{2}, b_{w} = 150mm, f_{pu} = 1500n/mm^{2}, b = 600mm, h_{t} = 250mm, design ultimate moment m_{ud} = 3400knm?

a) 9.5

b) 0.23

c) 6.7

d) 3.4

### View Answer

_{ps}= 3000mm

^{2}, d= 1150mm, f

_{cu}= 50n/mm

^{2}, b

_{w}= 150mm, f

_{pu }= 1500n/mm

^{2}, b = 600mm, h

_{t}= 250mm, design ultimate moment m

_{ud}= 3400knm, according to BS: 8110-1985,

_{Aps}= (A

_{pw}+A

_{pf}) = A

_{pf}= 0.45×50(600-150)(250/1500) = 0.45xf

_{cu}(b-b

_{w})(h

_{f}/f

_{pu}) = 1680mm

^{2}, A

_{pw }= (1300-1680) = 1320mm

^{2}, ratio(f

_{pu}A

_{pw}/f

_{cu}b

_{wd}) = (1500×1320/50x150x1150) = 0.23.

8. Calculate the slope of cable section at support uncracked in flexure given that eccentricity is 410, length is 30m and stress induced is 1000?

a) 0.0547

b) 2.456

c) 0.0234

d) 0.0123

### View Answer

9. Calculate the span section cracked in flexure (M=M0) F_{cp} = 23.4n/mm^{2}, z_{b} is 99×106 and stress induced is 1000?

a) 1200kn

b) 1850kn

c) 2300kn

d) 4300kn

### View Answer

_{cp}= 23.4n/mm

^{2}, zb is 99×10

^{6}, stress is 1000 m

_{0}= (0.8f

_{cp}Z

_{b}) = (0.8 x 23.4 x (99×10

^{6}/1000)) = 1850knm.

10. Find resultant maximum long term deflection if ϕ is 2.6, α_{y} is 38.5mm, α_{g} is 46mm, α_{p} is 74.7mm?

a) 95mm

b) 35mm

c) 55mm

d) 20mm

### View Answer

_{ce}= (E

_{c}/1+ϕ) = (E

_{c}/2.6), ϕ = 2.6, α

_{y}= 38.5mm, α

_{g}= 46mm, α

_{p}= 74.7mm, resultant maximum long term deflection = (2.6×46)+38.5-(0.85×74.7) = 95mm which is less than the code limit (span/250) = 120mm, ɳ = 0.85.

## Prestressed Concrete Structures MCQ Set 2

1. Design a pretensioned roof pull-in to suit the data F_{cu}, concrete cube strength = 50n/mm^{2}, effective span = 6m, applied load = 5kn/m, dead load = 1.4, live load = 1.6, β = 0.125, k = 7.5, Dc = 2400, and determine ultimate moment and shear?

a) 42 and 27.75

b) 54 and 27.75

c) 34 and 27.75

d) 20 and 28

### View Answer

_{min}/W

_{ud}= KD

_{c}gβ(L/h)L/f

_{cu}(d/h)

^{2}= 7.5×2400 x 9.81 x 0.125×25 x 6/50x 10

^{6}x(0.85)

^{2}= 0.094 F

_{cu}, concrete cube strength = 50n/mm

^{2}, effective span = 6m, applied load = 5kn/m, dead load = 1.4, live load = 1.6, β = 0.125, k = 7.5, D

_{c}= 2400, f

_{cu}= 50n/mm

^{2}, w

_{min}= (0.094)(9.25) = 0.86kn/m, m

_{u}= (0.125×9.25×6

^{2}) = 42knm, v

_{u }= (0.5×9.25×6) = 27.75kn.

2. Design cross sectional dimensions of pretensioned roof pull given that b is 0.5d?

a) 250

b) 260

c) 270

d) 280

### View Answer

_{u}= 0.10f

_{cu}bd

^{2}and if b = 0.5d D = (42×10

^{6}x2/0.10×50)

^{1/3}= 270mm.

3. Find the approximate thickness of web if b is 0.5d, d is 270mm, d/h ratio is 0.85, h is 315mm, adopt effective depth, d = 275mm overall depth , h is 320mm, width of flange of 160mm and Average thickness of flange is 70mm since sloping flanges are used, increases the flange thickness by 20 percent?

a) 45mm

b) 43mm

c) 41mm

d) 42mm

### View Answer

_{u}/f

_{t}h) = (0.85×27.75×10

^{3}/1.7×320) = 43mm.

4. Find minimum range of stresses if f_{ct} is 15n/mm^{2}, f_{cw} is 17, f_{tw} is zero, f_{u} is -1n/mm^{2}, ɳ is 0.8?

a) 12 and 18n/mm^{2}

b) 13 and 14n/mm^{2}

c) 12 and 15n/mm^{2}

d) 10 and 16n/mm^{2}

### View Answer

_{br}= (ɳf

_{ct}-f

_{cw}) = (0.85×15-0) = 12n/mm

^{2}, f

_{tr}= (f

_{cw }– ɳ

_{fu}) = (17-0.8x(-1)) = 17.8n/mm

^{2}, f

_{ct}= 15n/mm

^{2}, f

_{cw}= 17, f

_{tw}= 0, f

_{u}= -1n/mm

^{2}, ɳ = 0.8.

5. Find minimum section modulus given data is mg is 3.86×10^{6}, m_{q} is 22.50×10^{6}, f_{br} is given as 12 and the loss ratio is 0.8?

a) 134×10^{4}

b) 182×10^{4}

c) 123×10^{4}

d) 120×10^{4}

### View Answer

_{g}= 3.86×10

^{6}, m

_{q}= 22.50×10

^{6}, f

_{br}= 12, loss ratio = 0.8 Z

_{b}> or equal (m

_{q}+(1-ɳ)m

_{g}/f

_{br}) > or equal ((22.50×10

^{6})+(1-0.8)3.86×10

^{6})/12) Greater than equal to 182x104mm

^{3}.

6. Find the supporting force if given characteristic strength is -1, moment of gravity is 3.86×10^{6}, z_{t} = 230×10^{4}?

a) -2.68n/mm^{2}

b) -3.45n/mm^{2}

c) -1.23n/mm^{2}

d) 13.56n/mm^{2}

### View Answer

_{inf}Z

_{b}+f

_{sub}Z

_{t})/Z

_{t}+Z

_{b}) F

_{inf}= ((f

_{tw}/ɳ+(m

_{q}+m

_{g})/ɳz

_{b})) = ( 0+ (26.36×106/0.8x230x104)) F

_{sup}= (f

_{u}– m

_{g}/z

_{t}) = (-1 – (3.86×106)/(230×104)) = -2.68n/mm

^{2}.

7. Check for ultimate flexural strength if given A_{ps} is 154mm^{2}, f_{pu} is 1600n/mm^{2}, b is 160mm, f_{cu} is 50n/mm^{2}and diameter is 265mm?

a) 9.65

b) 0.116

c) 3.442

d) 2.345

### View Answer

_{ps}= (38.5xy) = 154mm

^{2}, f

_{pu}= 1600n/mm

^{2}, b = 160mm, f

_{cu}50n/mm

^{2},, d = 265mm (A

_{ps}f

_{pu}/bdf

_{cu}) = (154×1600/160x265x50) = 0.116.

8. Find ultimate shear strength (check it for safe against shear failure) if v_{u} is 27.75kn, Loss ratio is 0.8, prestressing force is 182000, area is 31400, breadth is 50 where height is 320, prestressing force is 1.7, f_{cp} = 4.65, f_{t} is 1.7?

a) Safe

b) Unsafe

c) Zero

d) Collapse

### View Answer

_{cp}= (ɳp/A) = (0.8×182000/31400) = 4.65n/mm

^{2}V

_{cw}= 0.67bh(f

_{1}

^{2}+0.8f

_{cp}f

_{t})

^{1/2}= (0.67x50x320(1.72+0.8×4.65×1.7)1/2/10

^{3}) = 33.2kn V

_{cw}> V

_{u}hence safe against shear failure.

9. Check for deflection due to prestressing force if given data is Prestressing force is 182×10^{3} eccentricity of cable is 10^{5}, Length of the cable is 1000, elastic modulus of concrete is 34×10^{3}, Moment of inertia is 3200×10^{5}?

a) 9.4

b) 4.5

c) 6.8

d) 9.8

### View Answer

^{3}e = 10

^{5}, L = 1000, elastic modulus of concrete = 34×10

^{3}, I = 3200×105 PeL

^{2}/8E

_{c}I = (182×10

^{3}x10

^{5}x6

^{2}x1000

^{2}/8x34x10

^{3}x3200x10

^{5}) = 6.8mm.

10. Find the deflection due to self weight given that ϕ = 1.6, E_{e} = 2.6E_{ce}, elastic modulus of concrete is 34×10^{3}, gravity is given as 6, self weight is 0.76, Length of the cable is 1000, elastic modulus of concrete is 34×10^{3} , Moment of inertia is 3200×10^{5}?

a) 1.66mm

b) 5.3mm

c) 23.4mm

d) 1.02mm

### View Answer

_{ce}= E

_{c}/1+ϕ, ϕ = 1.6, E

_{e}= 2.6E

_{ce}Deflection due to self weight g = (5gL

^{4}/384E

_{c}I) = (5×0.76×6

^{4}x1000

^{4}/384x34x10

^{3}x3700x10

^{5}) = 1.02mm.

## Prestressed Concrete Structures MCQ Set 3

1. The ultimate shear resistance for any given section, vc should be least of values:

a) v_{cw} and v_{cf}

b) v_{ew} and v_{ef}

c) v_{rw} and v_{rf}

d) v_{dw} and v_{df}

### View Answer

_{c}should be the least of values v

_{cw}and v

_{cf}where, v

_{cw = ultimate shear resistance of section cracked in web, vcf = ultimate shear resistance of section cracked in flange.}

2. What should be provided if the shear force due to ultimate load is less than the shear force of the concrete?

a) Tensile reinforcement

b) Shear reinforcement

c) Principle reinforcement

d) Compressive reinforcement

### View Answer

_{c}, the shear force which can be carried by the concrete, a minimum shear reinforcement should be provided in the form of stirrups with spacing.

3. The spacing provided for shear reinforcement is given as:

a) S_{v} = (A_{sv}0.87f_{y}/0.4b)

b) (A_{sv}0.91f_{y}/0.4b)

c) (A_{sv}0.12f_{y}/0.4b)

d) (A_{sv}0.23f_{y}/0.4b)

### View Answer

_{v}= (A

_{sv}0.87f

_{y}/0.4b), S

_{v}= spacing of stirrups along the length of member, A

_{sv}= cross sectional area of stirrup legs effective in shear, b = breadth (for T,I,L beams it is taken as breadth of rib, b

_{w}).

4. When the shear force due to ultimate loads is less than 0.5 times shear force of concrete then shear reinforcement is:

a) Provided

b) Not provided

c) Made equal

d) Made zero

### View Answer

_{c}) Then no shear reinforcement is provided in the members of low importance.

5. When v > v_{c} condition exits, then the shear reinforcement provided includes which extra terms than actual spacing equation?

a) f_{y}, d_{t}, v, v_{c}

b) f_{t}, d_{t}, v, v_{c}

c) d_{t}, v, v_{c}

d) f_{e}, d_{t}, v, v_{c}

### View Answer

_{c}shear reinforcement is required conforming to the relation (V > V

_{c}) The extra terms used are f

_{y}, d

_{t}, v, v

_{c}these are included in the spacing equation S

_{v}S

_{v}= (A

_{sv}0.87f

_{y}dt / V-V

_{c}).

6. The term dt in the spacing equation is termed as:

a) Lowest value of depth

b) Neutral value of depth

c) Highest value of depth

d) Peak value of depth

### View Answer

_{c}, the spacing provided in that: d

_{t}is the highest value of depth from the extreme compression fiber to longitudinal bars and depth from extreme compression fiber to centroid of tendons.

7. The spacing of stirrups for maximum shear stress is:

a) 0.9d_{t}

b) 0.10d_{t}

c) 0.12d_{t}

d) 0.7d_{t}

### View Answer

_{t}nor 4 times the web thickness of flanged members, for maximum shear stress the spacing of stirrups: S

_{v}> 0.75d

_{t}= > x web thickness.

8. The maximum spacing (S_{v})_{max} is provided for the condition:

a) V > 1.8V_{c}

b) V > 1.5V_{c}

c) V > 2.0V_{c}

d) V > 3.5V_{c}

### View Answer

_{c}, the maximum spacing should be reduced to 0.5d

_{t}, the lateral spacing of the individual legs of the stirrups provided at a cross section should not exceed 0.75d

_{t}, if V > 1.8V

_{c}, the maximum spacing is: (S

_{v}) max = 0.5 d

_{t}.

9. The maximum shear stress value for M_{35} and M_{50} is:

a) 3.5 and 4.0

b) 3.7 and 4.6

c) 3.8 and 6.0

d) 4.2 and 4.0

### View Answer

_{35}grade concrete is 3.7n/mm

^{2}, the maximum shear stress value for M

_{50}grade concrete is 4.6n/mm

^{2}, M

_{30}grade concrete is 3.5n/mm

^{2}, M

_{40}grade concrete is 4.0n/mm

^{2}, M

_{45}grade concrete is 4.3, M

_{55}grade concrete is 4.8n/mm

^{2}.

10. The section should be redesigned if the nominal shear stresses:

a) Exceeds the given values

b) Equal

c) Zero

d) Constant

### View Answer

^{2}) (IS: 1343-1980).

## Prestressed Concrete Structures MCQ Set 4

1. Which type of cables are advantages in reducing the effective shear?

a) Straight

b) Curved

c) Trapezoidal

d) Longitudinal

### View Answer

2. The various codes recommend empirical relations to estimate:

a) Ultimate shear resistance

b) Ultimate torsional resistance

c) Ultimate bending resistance

d) Ultimate load

### View Answer

3. Which type of shear reinforcement should be provided for members with thin webs?

a) Maximum shear reinforcement

b) Minimum shear reinforcement

c) Nominal shear reinforcement

d) Tensile reinforcement

### View Answer

4. The pre and post tensioned members with bonded tendons bond stress between:

a) Steel and concrete

b) Steel and water

c) Steel and aggregates

d) Steel and plastic

### View Answer

5. In case of pre tensioned member, the computations of transmission length is influenced by:

a) Bond

b) Flexure

c) Torsion

d) Tension

### View Answer

6. When prestress is transferred to concrete by means of external anchorages which pressure is developed:

a) Bearing

b) Twisting

c) Torsion

d) Bent

### View Answer

7. The bearing pressure on the concrete is given as:

a) 0.4f_{ci}

b) 0.8f_{ci}

c) 0.12f_{ci}

d) 0.2f_{ci}

### View Answer

_{ci}(A

_{br}/A

_{pan}) or 0.8 f

_{ci}, f

_{ci}= cube strength of concrete at transfer, A

_{br}= bearing area, A

_{pan}= punching area.

8. The effective punching area A_{pun} is generally the contact area of:

a) Tendon device

b) Anchorage device

c) Stress device

d) Strain device

### View Answer

9. The end block of a beam has a rectangular section 100mm wide by 200mm deep, the force of cable is 200kn. Find the actual bearing pressure?

a) 30n/mm^{2}

b) 40n/mm^{2}

c) 20n/mm^{2}

d) 10n/mm^{2}

### View Answer

_{br}= (100×100) = 10000mm

^{2}, Actual bearing pressure = (200×10

^{3}) / 10000 = 20n/mm

^{2}.

10. The end block of a prestressed concrete beam has a rectangular section; a cable carrying a force of 200kn is to be anchored against the end block at the centre if the cube strength of concrete at transfer is 30n/mm^{2}. Design the maximum permissible bearing pressure?(A_{br} = 10000mm^{2})

a) 24n/mm^{2}

b) 48n/mm^{2}

c) 54n/mm^{2}

d) 12n/mm2^{2}

### View Answer

_{pun}= (50×50) = 2500mm

^{2}, A

_{br}= 10000mm

^{2}, maximum permissible bearing pressure = 0.48fci(A

_{br}/A

_{pun}) or 0.8f

_{ci}whichever is smaller, f

_{b}= 0.48x30x(10000/2500)1/2 = 28.8n/mm

^{2}or ( 0.8×30) = 24n/mm2

^{2}.

## Prestressed Concrete Structures MCQ Set 5

1. The span of trusses generally lies in the range of:

a) 18-30m

b) 20-30m

c) 40-50m

d) 12-18m

### View Answer

2. The width of various components is kept constant at:

a) 100-200mm

b) 200-350mm

c) 150-300mm

d) 1200-1400mm

### View Answer

3. The bottom tie member should be sufficient size to:

a) Tension

b) Stress

c) House

d) Strain

### View Answer

4. The depth of diagonal web members is at a range of:

a) 100-150

b) 200-250

c) 110-210

d) 114-115

### View Answer

5. The use of concrete trusses with modular coordination for spans of 6and 9 are common for countries like:

a) America

b) Poland

c) India

d) Nueziland

### View Answer

6. The precast pretensioned cored slabs having circular or elliptical cavities have been used in:

a) France

b) Russia

c) Phillipines

d) Losangles

### View Answer

7. The prestressed concrete folded plate units are also widely used to cover roofs of:

a) Industrial buildings

b) Commercial buildings

c) Structural buildings

d) Regional buildings

### View Answer

8. Prestressed hollow inverted pyramids have been used as a transfer:

a) Girder system

b) Flange system

c) Block system

d) Chain system

### View Answer

9. Another example of application of prestressed concrete in buildings can be seen in construction of:

a) 11 – storied structure

b) 13 – storied structure

c) 10 – storied structure

d) 15 – storied structure

### View Answer

10. The design of joint should allow:

a) Retardation

b) Translation

c) Sublimination

d) Axial