Test 5 - Temperature Stresses and Thermal Deformation

Question 1 ప్రశ్న 1

A uniform prismatic bar is heated uniformly and is completely free to expand without any external axial load or restraint. Which statement is correct within the linear thermal-expansion range?

A The bar develops compressive stress equal to EαΔT. B The bar develops tensile stress equal to EαΔT. C The bar develops thermal strain αΔT but no thermal stress. D Both thermal strain and thermal deformation are zero.

Question 2 ప్రశ్న 2

A 2.5 m long steel bar is heated uniformly through 40°C and is completely free to expand. If α = 12 × 10^-6/°C, what is its increase in length?

A 0.60 mm B 1.20 mm C 2.40 mm D 4.80 mm

Question 3 ప్రశ్న 3

A uniform bar is fully restrained against axial deformation and undergoes a uniform temperature rise ΔT while remaining linearly elastic. Which expression gives the thermal stress, taking tension as positive?

A +EαΔT B -EαΔT C +αΔT/E D -αΔT/E

Question 4 ప్రశ్న 4

A steel bar is completely restrained between rigid supports and is heated uniformly by 75°C. If E = 200 GPa and α = 12 × 10^-6/°C, what thermal stress develops?

A 90 MPa tension B 120 MPa compression C 180 MPa compression D 240 MPa tension

Question 5 ప్రశ్న 5

An aluminium bar is fully restrained and then cooled uniformly by 40°C. If E = 70 GPa and α = 23 × 10^-6/°C, what thermal stress develops, assuming linear-elastic behaviour?

A 64.4 MPa tension B 64.4 MPa compression C 92.0 MPa tension D 92.0 MPa compression

Question 6 ప్రశ్న 6

A steel bar of area 600 mm² is fully restrained and subjected to a uniform temperature rise of 50°C. If E = 200 GPa and α = 12 × 10^-6/°C, what is the magnitude of the axial restraining force?

A 36 kN B 60 kN C 72 kN D 120 kN

Question 7 ప్రశ్న 7

A 2 m long steel bar is fixed at its left end and initially has a 0.72 mm gap between its right end and a rigid stop. The bar is heated by 80°C. If E = 200 GPa and α = 12 × 10^-6/°C, what compressive stress develops after contact with the stop?

A 48 MPa B 72 MPa C 120 MPa D 192 MPa

Question 8 ప్రశ్న 8

A 2.5 m long bar has one end fixed and a 1.2 mm gap at the other end before a rigid stop. If α = 12 × 10^-6/°C, what temperature rise is just sufficient to close the gap without producing stress?

A 20°C B 30°C C 40°C D 50°C

Question 9 ప్రశ్న 9

A steel bar 1000 mm long and 500 mm² in area has E = 200 GPa and α = 12 × 10^-6/°C. Its left end is fixed, while its right end is in contact with an initially unstressed axial spring of stiffness 50 kN/mm whose far end is fixed. If the bar is heated by 60°C, what compressive force develops?

A 18 kN B 24 kN C 36 kN D 72 kN

Question 10 ప్రశ్న 10

For the bar-and-spring system described by a heated bar pressing against a finite-stiffness spring, which statement is generally correct when the spring stiffness is positive and finite?

A The thermal stress must exceed that for complete rigid restraint. B The thermal stress is generally less than the complete-restraint value because some thermal movement is permitted. C No thermal stress can develop because the spring moves. D The thermal stress is independent of the spring stiffness.

Question 11 ప్రశ్న 11

A two-segment member is held between rigid supports. The steel segment has L = 1000 mm, A = 500 mm², E = 200 GPa and α = 12 × 10^-6/°C. The aluminium segment has L = 500 mm, A = 1000 mm², E = 70 GPa and α = 23 × 10^-6/°C. If the entire member is heated uniformly by 50°C, what compressive axial force develops?

A 50.0 kN B 68.5 kN C 85.0 kN D 117.5 kN

Question 12 ప్రశ్న 12

In a two-segment series member of different materials held between rigid supports and heated uniformly, with no intermediate external axial load, which statement is correct after restraint forces develop?

A Both segments necessarily have equal thermal stress. B Both segments carry the same axial force, but their stresses may differ if their areas differ. C Both segments necessarily undergo equal mechanical strain. D Each segment develops stress independently equal to -EαΔT regardless of the other segment.

Question 13 ప్రశ్న 13

An equal-length compound member consists of a steel core and an aluminium tube arranged concentrically, perfectly bonded so that they undergo the same axial strain, and assumed to remain straight without bending. The member is free from external axial load. Steel has A = 400 mm², E = 200 GPa and α = 12 × 10^-6/°C; aluminium has A = 600 mm², E = 70 GPa and α = 23 × 10^-6/°C. If the temperature rises uniformly by 50°C and both materials remain linearly elastic, what axial stresses develop approximately?

A Steel 37.9 MPa tension and aluminium 25.2 MPa compression B Steel 37.9 MPa compression and aluminium 25.2 MPa tension C Steel 120 MPa compression and aluminium 80.5 MPa compression D Both materials remain completely stress free

Question 14 ప్రశ్న 14

An equal-length concentric compound member consists of a steel core with A = 500 mm², E = 200 GPa and α = 12 × 10^-6/°C and an aluminium tube with A = 800 mm², E = 70 GPa and α = 23 × 10^-6/°C. The constituents are perfectly bonded and the member is completely restrained against any axial change in length. If its temperature rises uniformly by 40°C, what is the magnitude of the axial reaction at either rigid support?

A 48.0 kN B 51.5 kN C 80.0 kN D 99.5 kN

Question 15 ప్రశ్న 15

Two equal-length elastic materials with different Young's moduli but identical coefficients of thermal expansion are perfectly bonded together. The compound member is heated uniformly and is free from external axial load and external restraint. Which statement is correct?

A The higher-modulus material must develop compression. B The lower-modulus material must develop tension. C No thermal stress develops solely from the temperature change because both constituents have the same free thermal strain. D Equal coefficients of thermal expansion guarantee zero thermal deformation.

Question 16 ప్రశ్న 16

An equal-length compound member consists of a concentric steel core and aluminium tube that are perfectly bonded, remain straight without bending and therefore undergo the same axial strain. Steel has A = 400 mm², E = 200 GPa and α = 12 × 10^-6/°C; aluminium has A = 600 mm², E = 70 GPa and α = 23 × 10^-6/°C. The member is subjected to a uniform temperature rise of 50°C together with a concentric tensile load of 122 kN. Assuming both materials remain linearly elastic, what axial stresses develop approximately?

A Steel 237.9 MPa tension and aluminium 44.8 MPa tension B Steel 200 MPa tension and aluminium 70 MPa tension C Steel 37.9 MPa tension and aluminium 25.2 MPa compression D Steel 120 MPa compression and aluminium 80.5 MPa compression

Question 17 ప్రశ్న 17

A 1500 mm long steel bar is heated uniformly through 60°C. Its supports permit its length to increase by only 0.60 mm. If E = 200 GPa and α = 12 × 10^-6/°C, what thermal stress develops?

A 64 MPa tension B 64 MPa compression C 80 MPa compression D 144 MPa compression

Question 18 ప్రశ్న 18

A uniform bar is heated by ΔT, but its supports permit an actual expansion equal to exactly one-half of its unrestricted free thermal expansion. Assuming linear elasticity, what is the resulting thermal stress magnitude compared with the complete-restraint value EαΔT?

A Zero B One-fourth of EαΔT C One-half of EαΔT D Twice EαΔT

Question 19 ప్రశ్న 19

A 2 m long steel bar is free to expand and has a constant coefficient of thermal expansion α = 12 × 10^-6/°C. The temperature rise varies linearly along the bar from 0°C at one end to 60°C at the other. What is the total free thermal elongation?

A 0.36 mm B 0.72 mm C 1.44 mm D 2.40 mm

Question 20 ప్రశ్న 20

A uniform prismatic bar is completely restrained between rigid supports. Its temperature rise varies linearly along its length from 20°C at one end to 80°C at the other. If E = 210 GPa and α = 11 × 10^-6/°C are constant, what uniform axial stress develops under the one-dimensional linear-elastic model?

A 69.3 MPa compression B 92.4 MPa compression C 115.5 MPa compression D 184.8 MPa compression

Question 21 ప్రశ్న 21

Which statement about the coefficient of linear thermal expansion α is dimensionally correct?

A It has dimensions of stress. B It has dimensions of length per unit force. C It has units reciprocal to temperature, such as /°C or /K. D It is measured in MPa/°C.

Question 22 ప్రశ్న 22

A fully restrained steel bar has E = 200 GPa and α = 12 × 10^-6/°C. If the magnitude of thermal stress must not exceed 90 MPa, what is the maximum permissible magnitude of a uniform temperature change from the stress-free reference temperature?

A 25°C B 37.5°C C 45°C D 75°C

Question 23 ప్రశ్న 23

A linearly elastic steel bar held at fixed end separation initially has a uniform tensile stress of 50 MPa due to a pre-existing mechanical condition. Its temperature is then increased uniformly by 30°C while the end separation remains unchanged. If E = 200 GPa and α = 12 × 10^-6/°C, what is the final normal stress, taking tension as positive?

A 122 MPa tension B 72 MPa compression C 22 MPa tension D 22 MPa compression

Question 24 ప్రశ్న 24

Match the thermal-loading condition with the corresponding result for a uniform linearly elastic bar:
1. Free uniform heating
2. Fully restrained uniform heating
3. Fully restrained uniform cooling
4. Partial restraint allowing some but not all free expansion

P. Tensile thermal stress
Q. Thermal strain without thermal stress
R. Compressive stress smaller in magnitude than the complete-restraint value
S. Compressive stress of magnitude EαΔT

Which matching is correct?

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

Question 25 ప్రశ్న 25

Consider the following statements about thermal deformation and stress in axially loaded members:
1. A uniform freely heated bar can undergo thermal strain without developing thermal stress.
2. Complete restraint of uniform heating produces compressive stress in an initially stress-free bar.
3. In a one-dimensional, perfectly bonded two-material compound member that remains straight and is free of external axial force, different coefficients of thermal expansion can produce self-equilibrating internal axial stresses.
4. For a fully restrained uniform prismatic bar with constant E and α, the thermal stress EαΔT depends directly on the bar length and cross-sectional area.

Which statements are correct?

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

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