Concentric and Eccentric Pre Stressing

Q. A prestressed concrete beam 150 mm $\times$ 300 mm supports a live load 5 kN/m over a simple span of 8 m. It has a parabolic cable having an eccentricity of 75 mm at mid-span and zero at the ends. The prestressing force required to maintain the net resultant stress at the bottom fibre at mid-span as zero under the action of DL + LL + prestress is

1. 239 kN
2. 293 kN
3. 302 kN
4. 392 kN

Q. A prestressed concrete beam of cross-sectional area $A$, moment of inertial ${}^{\prime }{l}^{\prime }$, distance of top extreme fibre from neutral axis ${}^{\prime }{y}^{\prime }$ and distance of bottom extreme fibre from neutral axis ${}^{\prime }{y}_b^{\prime }$ is subjected to a prestressing force such that stress at top fibre is zero. What is the value of eccentricity ('r' is radius of gyration)?

1. $A/y_b$
2. $r^2/y_b$
3. $r^2/y_r$
4. $r{y}_b/y_t$

Q. Consider the following statements:
The shear resistance of structural concrete members may be improved by:

1. Axial prestressing
2. Vertical prestressing
3. Inclined prestressing

Which of these statements is/are correct?

1. 1 only
2. 1 and 2 only
3. 2 and 3 only
4. 1, 2 and 3

Q. In the PSC beam shown, $f_{ck}=45MPa$ and it supports a UDL of 15 kN/m including self weight. It is prestressed by a parabolic cable carrying an effective prestress of 200 kN. The shear resistance of uncracked section at the support will be

1. 93.8 kN
2. 94.5 kN
3. 94.4 kN
4. 95.4 kN

Q. In the prestressed concrete beam section shown in the given figure (all dimensions in mm in the figure), if the net losses are 15% and final prestressing force applied at 'A' is 500 kN, the initial extreme fibre stresses at tip and bottom will be respectively

1. $-3.40N/m{m}^{2}and16.70N/m{m}^2$
2. $-3.40N/m{m}^{2}and19.60N/m{m}^2$
3. $-4.0N/m{m}^{2}and16.70N/m{m}^2$
4. $-4.0N/m{m}^{2}and19.60N/m{m}^2$

Q. The cable for a prestressed concrete simply supported beam subjected to uniformly distributed load over the entire span span should ideally be

1. placed at the centre of cross-section over the entire span
2. placed at some eccentricity over entire span
3. varying linearly from the centre of cross-section at the ends to maximum eccentricity at the middle section
4. parabolic with zero eccentricity at the ends and maximum eccentricity at the centre of the span

Q. For a prestressed concrete continuous beam subject to different load combinations, which one of the following is correct for concordant cable profile?

1. It is not unique, but located in a narrow zone
2. It is unique
3. It is selected as compromise between secondary stresses and working stresses
4. It is selected based on deflection profile

Q. For a pretensioned rectangular plank the uplift at centre on release of wires from anchors due to pretensioning only (force P, eccentricity e) will be

1. $\frac{Pe{L}^2}{6EI}$
2. $\frac{P{e}^{2}L}{6EI}$
3. $\frac{Pe{L}^2}{8EI}$
4. $\frac{P{e}^{2}L}{8EI}$

Q. In prestressed concrete members, the shear force depends upon

1. Distributed load
2. Torsion
3. concentration load
4. variation in net bending moment

Q. A culvert is constructed with pretensioned inverted $T$ section and subsequent in situ concrete. Concrete grade corresponds to ${\sigma }_c=7MPa.$ For the section shown in the given figure, the maximum prestressing force will be

1. 620 kN
2. 890 kN
3. 970 kN
4. 1060 kN

Q. A concrete beam of rectangular cross-section of $200mm\times 400mm$ is prestressed with a force of 400 kN at an eccentricity of 100 mm. The maximum compressive stress in the concrete is

1. $12.5N/m{m}^2$
2. $7.5N/m{m}^2$
3. $5.0N/m{m}^2$
4. $2.5N/m{m}^2$

Q. When the tendon of a rectangular prestressed beam of cross-sectional area $A$ is subjected to a load $W$ through the centroidal longitudinal axis of beam, (where $M$ = maximum bending moment and $Z$ = section modulus) then the maximum stress in the beam section will be

1. $\frac{W}{A}-\frac{M}{Z}$
2. $\frac{W}{A}+\frac{M}{Z}$
3. $\frac{A}{W}-\frac{Z}{M}$
4. $\frac{A}{W}+\frac{Z}{M}$

Q. What is the uplift at centre on release of wires from anchors due to pretensioning only for force $P$ and eccentricity $e$ for a pre-tensioned rectangular plank?

1. $\frac{Pe{L}^2}{6EI}$
2. $\frac{P{e}^{2}L}{6EI}$
3. $\frac{Pe{L}^2}{8EI}$
4. $\frac{P{e}^{2}L}{8EI}$

Q. If the loading on a simply supported pre-stressed concrete beam is uniformly distributed, the centroid of tendons should be preferably

1. a straight profile along the centroidal axis
2. a straight profile along with the lower kern
3. a parabolic profile with convexity downward
4. a circular profile with convexity upward