Prestressed Concrete Beams Practice Questions

Consider a balanced doubly reinforced concrete section. If the material and other sectional properties remain unchanged, for which of the following cases will the section becomes under-reinforced?

A singly reinforced concrete beam of balanced section is made of M20 grade concrete and $\mathrm{Fe} 415$ grade steel bars. The magnitudes of the maximum compressive strain in concrete and the tensile strain in the bars at ultimate state under flexure, as per IS 456: 2000 are _______ respectively. (round off to four decimal places)

Consider a doubly reinforced RCC beam with the option of using either Fe250 plain bars or Fe500 deformed bars in the compression zone. The modulus of elasticity of steel is $2 \times 10^{5} \mathrm{~N} / \mathrm{mm}^{2}$ . As per IS456-2000, in which type(s) of the bars, the stress in the compression steel $\left(f_{s c}\right)$ can reach the design strength $\left(0.87 f_{y}\right)$ at the limit state of collapse?

A post-tensioned concrete member of span 15 m and cross-section of 450 mm x 450 mm is prestressed with three steel tendons, each of cross-sectional area 200 $mm^2$ . The tendons are tensioned one after another to a stress of 1500 MPa. All the tendons are straight and located at 125 mm from the bottom of the member. Assume the prestress to be the same in all tendons and the modular ratio to be 6. The average loss of prestress, due to elastic deformation of concrete, considering all three tendons is

A prismatic cantilever prestressed concrete beam of span length, L=1.5 m has one straight tendon placed in the cross-section as shown in the following figure (not to scale). The total prestressing force of 50 kN in the tendon is applied at $d_{c}=50 \mathrm{~mm}$ from the top in the cross-section of width, b=200 mm and depth, d=300 mm. If the concentrated load, P=5 kN, the resultant stress (in Mpa,in integer) experienced at point 'Q' will be _________

A concrete beam of span 15 m, 150 mm wide and 350 mm deep is prestressed with a parabolic cable as shown in the figure (not drawn to the scale). Coefficient of friction for the cable is 0.35, and coefficient of wave effect is 0.0015 per metre. If the cable is tensioned from one end only, the percentage loss (round off to one decimal place) in the cable force due to friction, is ________.

A simply supported prismatic concrete beam of rectangular cross-section, having a span of 8 m, is prestressed with an effective prestressing force of 600 kN. The eccentricity of the prestressing tendon is zero at supports and varies linearly to a value of e at the mid-span. In order to balance an external concentrated load of 12 kN applied at the mid-span, the required value of e (in mm, round off to the nearest integer) of the tendon, is _______.

A 3mx3m square precast reinforced concrete segments to be installed by pushing them through an existing railway embankment for making an underpass as shown in the figure. A reaction arrangement using precast PCC blocks placed on the ground is to be made for the jacks. At each stage, the jacks are required to apply a force of 1875 kN to push the segment. The jacks will react against the rigid steel plate placed against the reaction arrangement. The footprint area of reaction arrangement on natural ground is 37.5 $m^2$ . The unit weight of PCC block is 24 $kN/m^3$ . The properties of the natural ground are: c = 17 kPa; $\phi =25^{\circ}$ and $\gamma =18 kN/m^3$ . Assuming that the reaction arrangement has rough interface and has the same properties that of soil, the factor of safety (round off to 1 decimal place) against shear failure is _____

A 6 m long simply-supported beam is prestressed as shown in the figure. The beam carries a uniformly distributed load of 6 kN/m over its entire span. If the effective flexural rigidity $EI=2\times 10^{4}kN/m^{2}$ and the effective prestressing force is 200 kN, the net increase in length of the prestressing cable (in mm, up to two decimal places) is ______

A pre-tensioned rectangular concrete beam 150 mm wide and 300 mm depth is prestressed with three straight tendons, each having a cross-sectional area of 50 $mm^{2}$ , to an initial stress of 1200 $N / mm^{2}$ . The tendons are located at 100 mm from the soffit of the beam. If the modular ratio is 6, the loss of prestressing force (in kN, up to one decimal place) due to the elastic deformation of concrete only is ______

A simply supported rectangular concrete beam of span 8m has to be prestressed with a force of 1600 kN. The tendon is of parabolic profile having zero eccentricity at the supports. The beam has to carry an external uniformly distributed load of intensity 30 kN/m. Neglecting the self-weight of the beam, the maximum dip (in meters, up to two decimal places) of the tendon at the mid-span to balance the external load should be_______

In a pre-stressed concrete beam section shown in the figure, the net loss is 10% and the final pre-stressing force applied at X is 750 kN. The initial fiber stresses (in $N/mm^{2}$ ) at the top and bottom of the beam were:

A rectangular concrete beam 250mm wide and 600mm deep is pre-stressed by means of 16 high tensile wires, each of 7 mm diameter, located at 200mm from the bottom face of the beam at a given section. If the effective pre-stress in the wires is 700MPa, what is the maximum sagging bending moment (in kNm) (correct to 1-decimal place) due to live load that this section of the beam can with stand without causing tensile stress at the bottom face of the beam? Neglect the effect of dead load of beam.

Which one of the following is categorised as a long-term loss of prestress in a prestressed concrete member?

A concrete beam prestressed with a parabolic tendon is shown in the sketch. The eccentricity of the tendon is measured from the centroid of the cross-section. The applied prestressing force at service is 1620 kN. The uniformly distributed load of 45 kN/m includes the self-weight. The stress (in N/ $mm^2$ ) in the bottom fibre at mid-span is

As per India standard code of practice for pre stressed concrete (IS:1343-1980) the minimum grades of concrete to be used for post-tensioned and pre-tensioned structural elements are respectively

A rectangular concrete beam of width 120 mm and depth 200 mm is prestressed by pretensioning to a force of 150 kN at an eccentricity of 20 mm. The crosssectional area of the prestressing steel is 187.5 $mm^{2}$ . Take modulus of elasticity of steel and concrete as $2.1\times 10^{5}$ MPa and $3.0\times 10^{4}$ MPa respectively. The percentage loss of stress in the prestressing steel due to elastic deformation of concrete is

A pre-tensioned concrete member of section 200mm x 250mm contains tendons of area 500 $mm^{2}$ at centre of gravity of the section. The prestress in the tendons is 1000 $N/mm^{2}$ . Assuming modular ratio as 10, the stress ( $N/mm^{2}$ ) in concrete is

The percentage loss of prestress due to anchorage slip of 3 mm in a concrete beam of length 30 m which is post-tensioned by a tendon with an initial stress of 1200 $N/mm^{2}$ and modulus of elasticity equal to $2.1 \times 10^{5} N/mm^{2}$ is