Test 1 - Simple Stresses and Strains

Question 1 ప్రశ్న 1

A straight prismatic bar is subjected to a concentric axial tensile load P, and the stress distribution over a section sufficiently away from the load application is assumed uniform. Which expression gives the average normal stress?

A P × A B P/A C A/P D P/L

Question 2 ప్రశ్న 2

Using the common Strength of Materials sign convention in which tensile normal stress and tensile normal strain are positive, which statement is correct?

A Both tensile and compressive stresses are positive. B Tensile stress is negative and compressive stress is positive. C Tensile stress is positive and compressive stress is negative. D Normal stress has no sign because stress is always a scalar magnitude.

Question 3 ప్రశ్న 3

Which statement about the units and dimensions of normal stress and normal strain is correct?

A Stress has dimensions of force per area, while strain is dimensionless. B Both stress and strain have dimensions of force per area. C Stress is dimensionless, while strain has dimensions of length. D Stress has dimensions of force per length, while strain has dimensions of area.

Question 4 ప్రశ్న 4

A steel tie of uniform cross-sectional area 600 mm² carries a concentric tensile load of 120 kN. What is the average tensile stress in the tie?

A 50 MPa B 100 MPa C 120 MPa D 200 MPa

Question 5 ప్రశ్న 5

A 1500 mm long bar elongates by 0.75 mm under an axial tensile load. What is its longitudinal strain?

A 0.00025 B 0.00050 C 0.00100 D 0.00200

Question 6 ప్రశ్న 6

Within its linear elastic range, a material develops a normal stress of 150 MPa at a longitudinal strain of 0.00075. What is its Young's modulus?

A 100 GPa B 150 GPa C 200 GPa D 250 GPa

Question 7 ప్రశ్న 7

A uniform steel bar 2 m long and 400 mm² in cross-sectional area carries an axial tensile load of 80 kN. If E = 200 GPa, what is its elastic elongation?

A 2.0 mm B 4.0 mm C 8.0 mm D 10.0 mm

Question 8 ప్రశ్న 8

Using tension-positive deformation, a 2.5 m long steel member of area 750 mm² carries a concentric compressive load of 150 kN. If E = 200 GPa, what is its axial deformation?

A +1.25 mm B -1.25 mm C +2.50 mm D -2.50 mm

Question 9 ప్రశ్న 9

A material subjected to uniaxial tension has a longitudinal strain of +0.0012 and a lateral strain of -0.0003. What is its Poisson's ratio?

A 0.20 B 0.25 C 0.30 D 0.40

Question 10 ప్రశ్న 10

A circular steel rod of diameter 40 mm is subjected to a tensile stress of 120 MPa. If E = 200 GPa and Poisson's ratio ν = 0.30, what is the approximate change in diameter within the linear elastic range?

A Increase of 0.0240 mm B Decrease of 0.0240 mm C Decrease of 0.0072 mm D Increase of 0.0072 mm

Question 11 ప్రశ్న 11

An isotropic linearly elastic material is subjected to a uniaxial tensile stress of 120 MPa. If E = 200 GPa and ν = 0.30, what is the approximate volumetric strain under the small-strain assumption?

A 0.00024 B 0.00042 C 0.00060 D 0.00120

Question 12 ప్రశ్న 12

A 100 mm × 100 mm × 100 mm cube of an isotropic linearly elastic material is subjected to uniaxial tensile stress of 100 MPa. If E = 200 GPa and ν = 0.25, what is the approximate increase in volume, neglecting products of strains?

A 50 mm³ B 100 mm³ C 125 mm³ D 250 mm³

Question 13 ప్రశ్న 13

A stepped steel bar carries a constant tensile force of 60 kN. Segment 1 is 1000 mm long with area 300 mm², and Segment 2 is 1500 mm long with area 600 mm². If E = 200 GPa throughout, what is the total elongation?

A 1.25 mm B 1.75 mm C 2.25 mm D 3.50 mm

Question 14 ప్రశ్న 14

A 20 mm diameter steel rod of length 3 m has E = 200 GPa. The tensile stress must not exceed 120 MPa and the elongation must not exceed 1.5 mm. What is the maximum permissible axial tensile load considering both limits?

A 25.1 kN B 37.7 kN C 31.4 kN D 62.8 kN

Question 15 ప్రశ్న 15

A circular prismatic bar remains within the linear elastic range while carrying the same axial load P over the same length. If its diameter is doubled without changing the material, what happens to both its average normal stress and its axial deformation?

A Both become one-fourth of their original values. B Both become one-half of their original values. C Stress becomes one-fourth but deformation remains unchanged. D Stress remains unchanged but deformation becomes one-fourth.

Question 16 ప్రశ్న 16

A stepped axial member carries the same internal tensile force through two adjacent segments, with no external load applied between them. Segment A has twice the cross-sectional area of Segment B. Which statement about their average normal stresses is correct?

A Both segments have the same stress because the internal force is the same. B The average stress in Segment B is twice that in Segment A. C The average stress in Segment A is twice that in Segment B. D Their stresses cannot be compared without knowing Young's modulus.

Question 17 ప్రశ్న 17

Consider the following statements about simple axial stress and strain:
1. Average normal stress under concentric axial loading is P/A.
2. Longitudinal normal strain is dimensionless.
3. Elastic axial deformation of a prismatic bar under a given P, L and A is independent of Young's modulus.
4. Within the linear proportional range, normal stress is proportional to normal strain.

Which statements are correct?

A 1 and 3 only B 2 and 4 only C 1, 2 and 4 only D 1, 2, 3 and 4

Question 18 ప్రశ్న 18

Match the quantity with the appropriate simple relationship for the stated elementary loading conditions:
1. Average normal stress
2. Longitudinal strain
3. Poisson's ratio
4. Elastic elongation of a uniform prismatic bar

P. δ/L
Q. PL/(AE)
R. P/A
S. - lateral strain/longitudinal strain

Which matching is correct?

A 1-P, 2-R, 3-Q, 4-S B 1-Q, 2-S, 3-P, 4-R C 1-S, 2-Q, 3-R, 4-P D 1-R, 2-P, 3-S, 4-Q

Question 19 ప్రశ్న 19

A 20 mm diameter pin transmits a load of 100 kN through a connection in double shear. Assuming the load is shared equally by the two shear planes, what is the average direct shear stress in the pin?

A 79.6 MPa B 159.2 MPa C 318.3 MPa D 636.6 MPa

Question 20 ప్రశ్న 20

A 20 mm diameter pin carries a total load of 90 kN equally through three direct shear planes. What is the average shear stress on each resisting plane?

A 95.5 MPa B 143.2 MPa C 191.0 MPa D 286.5 MPa

Question 21 ప్రశ్న 21

Which statement most accurately describes the applicability of the elementary form of Hooke's law, σ = Eε, in an axial stress-strain test?

A It applies to every stress level up to fracture. B It applies only after permanent deformation has started. C It represents the linear proportional stress-strain relationship within the material's proportional range. D It requires strain to remain constant as stress increases.

Question 22 ప్రశ్న 22

Two prismatic bars have the same length and carry the same axial tensile load. Bar A has E = 200 GPa and area 300 mm², while Bar B has E = 100 GPa and area 600 mm². Neglecting all other effects, which statement about their elastic elongations is correct?

A Bar A elongates twice as much as Bar B. B Bar B elongates twice as much as Bar A. C Bar B elongates four times as much as Bar A. D The two bars have equal elongation.

Question 23 ప్రశ్న 23

An aluminium bar is 1500 mm long, has an area of 600 mm² and Young's modulus E = 70 GPa. What axial tensile load will produce an elastic elongation of 1.8 mm?

A 42.0 kN B 50.4 kN C 63.0 kN D 84.0 kN

Question 24 ప్రశ్న 24

A two-segment steel bar has E = 200 GPa throughout. Segment AB is 800 mm long with area 500 mm² and carries 100 kN tension, while Segment BC is 1200 mm long with area 400 mm² and carries 40 kN compression. Taking elongation as positive, what is the algebraic change in the total length?

A +0.20 mm B -0.20 mm C +1.40 mm D -1.40 mm

Question 25 ప్రశ్న 25

Consider the following statements for an isotropic material under small, uniaxial, linear-elastic deformation using tension-positive normal strain:
1. Tensile longitudinal strain is positive.
2. For an ordinary material with positive Poisson's ratio, lateral strain under uniaxial tension has the same sign as longitudinal strain.
3. To first order, volumetric strain is the sum of three mutually perpendicular normal strains.
4. For a uniform axial bar with fixed P, L and A, doubling Young's modulus halves its elastic deformation.

Which statements are correct?

A 1 and 2 only B 2, 3 and 4 only C 1, 3 and 4 only D 1, 2, 3 and 4

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