Engineering Questions with Answers - Multiple Choice Questions
Stress Distribution – Triangular Loadings
1 - Question
The uniformly varying load is __________ in a beam.
a) rate of loading increases linearly from zero
b) rate of loading increases non-linearly from zero
c) equal load at every point
d) equal load only at supports
View Answer
Answer: a
Explanation: The uniformly varying load is the rate of loading which increases linearly from zero at one end of the support.
2 - Question
The triangular load is also known as ___________
a) uniformly distributed load
b) uniformly varying load
c) point load
d) equivalent uniformly distributed load
View Answer
Answer: b
Explanation: The triangular load is also known as uniformly varying load. The uniformly varying load is the rate of loading which increases linearly from zero at one end of the support.
3 - Question
For any position of point P subtending angle α with AB, the vertical stress is given by___________
a) σz=qaπ[xα(x−α)]
b) σz=qaπ
c) σz=qaπ[xα−az(x−α)2+z2(x−α)]
d) σz=[xα−az(x−α)2+z2(x−α)]
View Answer
Answer: c
Explanation: For any position of point P subtending angle α with AB, the vertical stress is given by,
σz=qaπ[xα−az(x−α)2+z2(x−α)]
Where, σz= vertical stress
x=distance from the support A
z=depth from the ground surface
q=load applied.
4 - Question
For point P under the support A, the vertical stress is given by __________
a) σz=qaπ[xα(x−α)]
b) σz=qaπ
c) σz=qπ[aza2+z2]
d) σz=[xα−az(x−α)2+z2(x−α)]
View Answer
Answer: c
Explanation: For point P under the support A, the vertical stress is given by,
σz=qπsin2αA2
∴ σz=qπ[aza2+z2].
5 - Question
For point P under the support B, the vertical stress is given by __________
a) σz=qaπ[xα(x−α)]
b) σz=qπαB
c) σz=qπ[aza2+z2]
d) σz=[xαB−az(x−αB)2+z2(x−αB)]
View Answer
Answer: b
Explanation: For point P under the support B, the vertical stress is given by,
σz=qπαB
Where α_B=angle subtended from point P below the support B to the line AB
q=load applied.
6 - Question
For a linearly variable infinite load, for a point P, the vertical stress σz is _________
a) σz=qaπ[xα+z]
b) σz=qaπ
c) σz=qπ[aza2+z2]
d) σz=[xα−az(x−α)2+z2(x−α)]
View Answer
Answer: a
Explanation: let the load intensity be q at a horizontal distance a and the load intensity at distance x is qx=q*x/a.
∴ for any point P the load is given by, σz=qaπ[xα+z].
7 - Question
For a symmetrically distributed triangular load, under the centre of the triangular load, the vertical stress at any point at a depth z is given by ___________
a) σz=qaπ[α1+α2]
b) σz=qπ[α1+α2]
c) σz=qπ[aza2+z2]
d) σz=qπ[α1−α2]
View Answer
Answer: b
Explanation: Considering two triangular loads of AOC and OCB separately and adding them we get,
σz1=qπα1 for triangular load of AOC
σz2=qπα2 for triangular load of OCB
∴ σz=σz1+σz2
∴ σz=qπ[α1+α2].
8 - Question
For a symmetrically distributed triangular load, the shear stress τxz at any point at a depth z is given by ___________
a) τxz=−qzaπ[α1−α2]
b) τxz=−qπ[α1+α2]
c) τxz=−qπ[aza2+z2]
d) τxz=−qπ[α1−α2]
View Answer
Answer: a
Explanation: For a symmetrically distributed triangular load, the shear stress τxz at any point at a depth z is given by,
τxz=−qzaπ[α1−α2]where α1 and α2 are angles subtended by the point P at AO and BO respectively
z=depth.
9 - Question
For a triangular and uniformly distributed semi-infinite loads, the shear stress τxz in the plane xz is ___________
a) τxz=−qzaπα
b) τxz=−qπα
c) τxz=−qπ[aza2+z2]
d) τxz=−qπz
View Answer
Answer: a
Explanation: For a triangular and uniformly distributed semi-infinite loads, the shear stress τxz in the plane xz is given by,
τxz=−qzaπ α where α is the angle subtended by point P on OA,
z=depth
q=load intensity.
10 - Question
For a load intensity of q=20kN/m, find the shear stress τxz at a depth 5m from the given diagram.
a) -5.2 kN/m2
b) -6.2 kN/m2
c) -7.2 kN/m2
d) -8.2 kN/m2
View Answer
Answer: b
Explanation: Given,
Load q=20kN/m
α=30°=0.523rad
a=2.68m
z=5m
∴ τxz=−qzaπα
τxz=−20∗52.68∗π0.523
τxz=-6.2 kN/m2.
11 - Question
For a triangular and uniformly distributed semi-infinite loads, the vertical stress σz is given by ___________
a) σz=qaπ[xα+z]
b) σz=qaπ(aβ+xα)
c) σz=qπ[aza2+z2]
d) σz=[xα−az(x−α)2+z2(x−α)]
View Answer
Answer: b
Explanation: For a triangular and uniformly distributed semi-infinite loads, the vertical stress σz is given by,
σz=qaπ(aβ+xα) where α is the angle subtended by point P on OA,
β= angle at point P between horizontal line and PA
q=load intensity.
12 - Question
For a load intensity of q=20kN/m, find the vertical stress σz from the given diagram.
a) 5.62 kN/m2
b) 6.23 kN/m2
c) 13.33 kN/m2
d) 8.32 kN/m2
View Answer
Answer: c
Explanation: Given,
Load q=20kN/m
α=60°=1.047rad
β=60°=1.047rad
a=2.68m
the vertical stress σz is,
σz=qaπ(aβ+xα)
σz=202.68∗π(2.68∗1.047+2.68∗1.047)
∴ σz=13.33 kN/m2.
13 - Question
Trapezoidal load is encountered in earth fills.
a) True
b) False
View Answer
Answer: a
Explanation: Trapezoidal loadings are quite commonly encountered in earth fills, embankments, highways, rail road, earth dams, etc. The trapezoidal loadings can be split into a triangular loading minus another triangular loading of smaller magnitude.
14 - Question
The maximum shear stress is the difference between major and minor principal stresses.
a) True
b) False
View Answer
Answer: b
Explanation: The maximum shear stress is half the difference between major and minor principal stresses.
τmax=12(σ1−σ2).
15 - Question
The greatest value of maximum shear stress τmax occurs when angle θ is _________
a) π
b) π/2
c) π/3
d) π/4
View Answer
Answer: b
Explanation: The maximum shear stress is given by,
τmax=12(σ1−σ2)=qπsinθ
Sinθ is maximum when θ= π/2
∴ Sin π/2=1
∴ τmax=qπ.