# Prestressed Concrete Structures Questions and Answers – Design of Pretensioned Beams

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This set of Prestressed Concrete Structures Multiple Choice Questions & Answers (MCQs) focuses on “Design of Pretensioned Beams”.

1. Design a pretensioned roof pull-in to suit the data Fcu, concrete cube strength = 50n/mm2, 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

Explanation: Wmin/Wud = KDcgβ(L/h)L/fcu(d/h)2 = 7.5×2400 x 9.81 x 0.125×25 x 6/50x 106x(0.85)2 = 0.094
Fcu, concrete cube strength = 50n/mm2, effective span = 6m, applied load = 5kn/m, dead load = 1.4, live load = 1.6, β = 0.125, k = 7.5, Dc = 2400, fcu = 50n/mm2, wmin = (0.094)(9.25) = 0.86kn/m, mu = (0.125×9.25×62) = 42knm, vu = (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

Explanation: Mu = 0.10fcubd2 and if b = 0.5d
D = (42×106x2/0.10×50)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

Explanation: b = 0.5d, d = 270mm, d/h = 0.85, h = 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:
Thickness of flange = (0.2×275) =55mm Approximate thickness of web = (0.85vu/fth) = (0.85×27.75×103/1.7×320) = 43mm.

4. Find minimum range of stresses if fct is 15n/mm2, fcw is 17, ftw is zero, fu is -1n/mm2, ɳ is 0.8?
a) 12 and 18n/mm2
b) 13 and 14n/mm2
c) 12 and 15n/mm2
d) 10 and 16n/mm2

Explanation: Range of stress fbr = (ɳfct-fcw) = (0.85×15-0) = 12n/mm2, ftr = (fcw – ɳfu) = (17-0.8x(-1)) = 17.8n/mm2, fct = 15n/mm2, fcw = 17, ftw = 0, fu = -1n/mm2, ɳ = 0.8.

5. Find minimum section modulus given data is mg is 3.86×106, mq is 22.50×106, fbr is given as 12 and the loss ratio is 0.8?
a) 134×104
b) 182×104
c) 123×104
d) 120×104

Explanation: mg = 3.86×106, mq = 22.50×106, fbr = 12, loss ratio = 0.8
Zb > or equal (mq+(1-ɳ)mg/fbr) > or equal ((22.50×106)+(1-0.8)3.86×106)/12)
Greater than equal to 182x104mm3.

6. Find the supporting force if given characteristic strength is -1, moment of gravity is 3.86×106, zt = 230×104?
a) -2.68n/mm2
b) -3.45n/mm2
c) -1.23n/mm2
d) 13.56n/mm2

Explanation: p = (A(finfZb+fsubZt)/Zt+Zb)
Finf = ((ftw/ɳ+(mq+mg)/ɳzb)) = (0+ (26.36×106/0.8x230x104))
Fsup = (fu – mg/zt) = (-1 – (3.86×106)/(230×104)) = -2.68n/mm2.

7. Check for ultimate flexural strength if given Aps is 154mm2, fpu is 1600n/mm2, b is 160mm, fcu is 50n/mm2and diameter is 265mm?
a) 9.65
b) 0.116
c) 3.442
d) 2.345

Explanation: Aps = (38.5xy) = 154mm2, fpu = 1600n/mm2, b = 160mm, fcu 50n/mm2, d = 265mm
(Apsfpu/bdfcu) = (154×1600/160x265x50) = 0.116.

8. Find ultimate shear strength (check it for safe against shear failure) if vu 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, fcp = 4.65, ft is 1.7?
a) Safe
b) Unsafe
c) Zero
d) Collapse

Explanation: Fcp = (ɳp/A) = (0.8×182000/31400) = 4.65n/mm2
Vcw = 0.67bh(f12+0.8fcpft)1/2 = (0.67x50x320(1.72+0.8×4.65×1.7)1/2/103) = 33.2kn
Vcw > Vu hence safe against shear failure.

9. Check for deflection due to prestressing force if given data is Prestressing force is 182×103 eccentricity of cable is 105, Length of the cable is 1000, elastic modulus of concrete is 34×103, Moment of inertia is 3200×105?
a) 9.4
b) 4.5
c) 6.8
d) 9.8

Explanation: P = 182×103 e = 105, L = 1000, elastic modulus of concrete = 34×103, I = 3200×105
PeL2/8EcI = (182×103x105x62x10002/8x34x103x3200x105) = 6.8mm.

10. Find the deflection due to self weight given that ϕ = 1.6, Ee = 2.6Ece, elastic modulus of concrete is 34×103, gravity is given as 6, self weight is 0.76, Length of the cable is 1000, elastic modulus of concrete is 34×103 , Moment of inertia is 3200×105?
a) 1.66mm
b) 5.3mm
c) 23.4mm
d) 1.02mm 