1. A rectangular concrete beam of cross section 120mm wide and 300mm deep is prestressed by a straight cable, effective force of 180kn at an eccentricity 50, area of 36×103mm2(z=18×105mm3). Find the total stress due to prestress?
a) 10
b) 25
c) 35
d) 45
Explanation: P = 180kn, A = 36×103mm2, e = 50mm, b = 120mm, d = 300mm, z = 18×105mm3
Stresses due to prestress = (p/a) = (180×103/36×103) = 5n/mm2, (pe/z) = (180×103×50/18×105) = 5n/mm2
Total stress = ((p/a)+(pe/z))=(5+5) = 10n/mm2
2. A rectangular concrete beam of cross section 100mm wide and 400mm deep is prestressed by a straight cable of span 6m, imposed load is 3.14kn/m, area is 36×103mm2(Z=18×105mm3). Calculate working moment assuming the self weight of concrete as 24kn/m3?
a) 10.25
b) 2.25
c) 3.25
d) 4.25
Explanation: Z = 18×105mm3, A = 36×103mm2, G = (0.1×0.4×24) = 0.96kn/m
Total load W = (g+q) = (0.96+3.14) = 4.1kn/m, Maximum working moment = (0.125×4×62) = 18.45knm
(M/Z) = (18.45×106/18×105) = 10.25n/mm2.
3. When the tensile stresses are developed in the cracks, they are visible at ____________
a) Hoop stress of beams
b) Soffit of beams
c) Sagging of beams
d) Hogging of beams
Explanation: The tensile stresses are developed when cracks become visible at the soffit of beams depend upon the type and distribution of steel reinforcement and the quality of concrete in beam, at the soffit of the beam concrete behaves according to influencing parameters of steel reinforcement.
4. The cracks appear when the tensile stresses at the soffit are equal to ____________
a) Modulus of elasticity
b) Modulus of rupture
c) Tension modulus
d) Reinforcement modulus
Explanation: It is generally considered that visible cracks appear when the tensile stresses at the soffit are approximately equal to modulus of rupture of the material, it is an ultimate strength pertaining to failure of beams by flexure equal to the bending moment at rupture divided by the section modulus of beams.
5. The widths of the cracks are influenced by ____________
a) Degree of bond
b) Stress
c) Strain
d) Tension
Explanation: The widths of the cracks are highly influenced by the degree of bond developed between concrete and steel and stress corrosion cracking results from the combined action of corrosion and static tensile stress which may be either residual or externally applied.
6. The formulae for load factor against cracking is ____________
a) Cracking moment/Working moment
b) Cracking moment/Bending moment
c) Cracking moment/Tensile moment
d) Cracking moment/Aerial moment
Explanation: The beam at which visible cracks developed in prestressed concrete members is generally referred to as the “cracking moment” and their formula for load factor against cracking is cracking moment/working moment
7. The loss of prestress due to elastic deformation of concrete depends on ____________
a) Modular ratio and average stress
b) Modular elasticity and shear
c) Prestress in concrete
d) Modulus of elasticity of steel
Explanation: The loss due to elastic deformation of concrete depends on the modular ratio and the average stress in concrete at the level of steel, consider a post tensioned member which is prestressed by a single tendon and the shortening of concrete occurs till the tendon is jacked and no shortening of concrete is observed after it
8. The term Ec in losses developed by elastic deformation is expressed as ____________
a) Pe/A
b) Pc/Ea
c) P/AcEc
d) Ea/El
Explanation: The term Ec is defined as strain in concrete and the equation for loss due to elastic deformation is given as Ec = Pc/Ec = P/Ac×1/Ec, the tension in the tendon is obtained after the elastic shortening of concrete and therefore, there will not be losses due to elastic shortening.
9. The term Es in losses developed by elastic deformation is defined as ____________
a) Shear in steel
b) Torsion in steel
c) Strain loss in steel
d) Loading in steel
Explanation: The term Es is defined as strain loss in steel, Es = Δfs/Es,
Δfs = Loss of stress in steel, Es = strain loss in steel.
10. The loss of stress in steel due to elastic shortening or deformation is ____________
a) αefc
b) αcfc
c) αc/fc
d) αe/fc
Explanation: Loss of stress in steel due to elastic shortening is αefc,
αe = Es/Ec = modular ratio, fc = prestress in concrete at the level of steel, Es = modulus of elasticity of steel, Ec = modulus of elasticity of concrete