Test 3 - Axially Loaded and Stepped Bars

Question 1 ప్రశ్న 1

A stepped member consists of several prismatic segments connected in series and remains within the linear-elastic range. If segment i carries constant axial force Ni over length Li and has area Ai and Young's modulus Ei, which expression gives the algebraic total axial deformation?

A Σ(NiAi)/(LiEi) B Σ(NiLi)/(AiEi) C Σ(AiEi)/(NiLi) D Σ(NiEi)/(AiLi)

Question 2 ప్రశ్న 2

A uniform steel bar 2 m long and 500 mm² in area carries a tensile load of 100 kN. If E = 200 GPa, what is its elastic elongation?

A 1.0 mm B 2.0 mm C 4.0 mm D 5.0 mm

Question 3 ప్రశ్న 3

A stepped steel bar carries a constant tensile force of 80 kN. One segment is 800 mm long with area 400 mm² and the second is 1200 mm long with area 800 mm². If E = 200 GPa throughout, what is the total elongation?

A 0.80 mm B 1.00 mm C 1.40 mm D 2.00 mm

Question 4 ప్రశ్న 4

A two-segment bar carries a constant tensile force of 60 kN. The first segment is steel with L = 1000 mm, A = 500 mm² and E = 200 GPa, while the second is aluminium with L = 800 mm, A = 800 mm² and E = 70 GPa. What is the total elongation?

A 1.20 mm B 1.46 mm C 1.80 mm D 2.10 mm

Question 5 ప్రశ్న 5

A stepped bar ABC is fixed at A. At B, a 30 kN axial load acts toward A, while at free end C a 90 kN load acts away from A. Segment AB has L = 1000 mm and A = 600 mm², while BC has L = 800 mm and A = 400 mm². If E = 200 GPa throughout, what is the displacement of C relative to A?

A 0.90 mm elongation B 1.10 mm elongation C 1.40 mm elongation D 1.80 mm elongation

Question 6 ప్రశ్న 6

A bar ABC is fixed at A. Axial loads of 40 kN and 70 kN act to the right at B and C respectively. The areas of segments AB and BC are 550 mm² and 350 mm² respectively. What are the average normal stresses in AB and BC?

A AB = 200 MPa tension and BC = 200 MPa tension B AB = 127.3 MPa tension and BC = 314.3 MPa tension C AB = 200 MPa compression and BC = 200 MPa tension D AB = 127.3 MPa tension and BC = 200 MPa tension

Question 7 ప్రశ్న 7

A bar ABC is fixed at A. A load of 80 kN acts to the right at B and a load of 30 kN acts to the left at free end C. Segment AB has L = 1200 mm and A = 500 mm², while BC has L = 800 mm and A = 400 mm². For E = 200 GPa, what is the algebraic displacement of C, taking elongation as positive?

A -0.90 mm B -0.30 mm C +0.30 mm D +0.90 mm

Question 8 ప్రశ్న 8

Two adjacent segments of an axially loaded member undergo opposite deformations. Segment AB carries 80 kN tension and has L = 1000 mm, A = 500 mm² and E = 200 GPa. Segment BC carries 40 kN compression, has L = 800 mm and the same E. What area must BC have so that the total end-to-end deformation is zero?

A 100 mm² B 200 mm² C 250 mm² D 400 mm²

Question 9 ప్రశ్న 9

Two prismatic bars have the same length and carry the same tensile load. Bar 1 has A = 400 mm² and E = 200 GPa, while Bar 2 has A = 800 mm² and E = 100 GPa. Which statement concerning their elastic elongations is correct?

A Bar 1 elongates twice as much as Bar 2. B Bar 2 elongates twice as much as Bar 1. C Both bars have the same elongation. D The elongations cannot be compared without knowing the load magnitude.

Question 10 ప్రశ్న 10

A stepped bar ABC is fixed at A. A 20 kN load acts toward A at B, and an 80 kN load acts away from A at C. Segment AB has L = 1000 mm and A = 600 mm², while BC has L = 800 mm and A = 400 mm². If E = 200 GPa, what are the displacements of B and C relative to A?

A uB = 0.50 mm and uC = 1.30 mm B uB = 0.80 mm and uC = 1.30 mm C uB = 0.50 mm and uC = 0.80 mm D uB = 0.30 mm and uC = 1.10 mm

Question 11 ప్రశ్న 11

A two-segment member carries the same tensile load P throughout. Segment 1 has L = 1000 mm, A = 400 mm² and E = 200 GPa. Segment 2 has L = 800 mm, A = 600 mm² and E = 70 GPa. What value of P will produce a total elongation of 2.0 mm?

A 50.0 kN B 63.4 kN C 80.0 kN D 100.0 kN

Question 12 ప్రశ్న 12

A two-segment bar carries a constant tensile force of 50 kN. Segment 1 has L = 800 mm, A = 400 mm² and E = 200 GPa. Segment 2 has L = 1000 mm, A = 500 mm² and unknown Young's modulus E2. If the total elongation is 1.50 mm, what is E2?

A 50 GPa B 75 GPa C 100 GPa D 150 GPa

Question 13 ప్రశ్న 13

Two steel segments are connected in series and carry the same axial load. Segment 1 has L = 1000 mm and A = 400 mm², while Segment 2 has L = 500 mm and A = 800 mm². If E = 200 GPa, what is the equivalent axial stiffness P/δ of the complete member?

A 32 kN/mm B 48 kN/mm C 64 kN/mm D 80 kN/mm

Question 14 ప్రశ్న 14

Every cross-sectional area of a stepped linear-elastic bar is doubled, while its segment lengths, Young's moduli and internal axial forces remain unchanged. What happens to its total axial deformation?

A It doubles. B It becomes one-half. C It becomes one-fourth. D It remains unchanged.

Question 15 ప్రశ్న 15

A straight bar is subjected only to concentrated axial loads and has no distributed axial loading between them. Which statement about the internal axial force is correct?

A It must vary linearly within every segment. B It is constant between adjacent concentrated-load points and changes when an axial concentrated load is crossed. C It is always equal to the largest applied load everywhere in the member. D It depends only on cross-sectional area and not on equilibrium.

Question 16 ప్రశ్న 16

At an abrupt change in cross-section of an axially loaded stepped bar, how should the elementary stress expression P/A be interpreted?

A It gives the exact pointwise stress everywhere at the geometric discontinuity. B It gives a nominal average normal stress away from the local stress-concentration region. C It becomes invalid throughout both complete segments. D It can be used only when Young's modulus is zero.

Question 17 ప్రశ్న 17

Match the axial-member quantity with its appropriate expression for a prismatic elastic segment:
1. Average normal stress
2. Axial rigidity
3. Axial compliance of a segment
4. Segment deformation

P. AE
Q. N/A
R. L/(AE)
S. NL/(AE)

Which matching is correct?

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

Question 18 ప్రశ్న 18

Consider the following statements about stepped axially loaded members:
1. With tension taken positive, the sign of NL/(AE) follows the sign of internal axial force N when A, E and L are positive.
2. Adjacent segments necessarily carry the same internal axial force even when a concentrated axial load acts at their junction.
3. For fixed N and L, increasing AE reduces the magnitude of elastic axial deformation.
4. Total end-to-end deformation is obtained by the algebraic sum of segment deformations.

Which statements are correct?

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

Question 19 ప్రశ్న 19

A stepped circular steel bar carries a constant tensile load of 60 kN. The first segment is 500 mm long and 20 mm in diameter, while the second is 1000 mm long and 30 mm in diameter. If E = 200 GPa, what is the total elongation approximately?

A 0.451 mm B 0.902 mm C 1.804 mm D 2.405 mm

Question 20 ప్రశ్న 20

Two segments connected in series carry the same axial tensile force P. Segment 1 has area 300 mm² and allowable tensile stress 150 MPa, while Segment 2 has area 500 mm² and allowable tensile stress 120 MPa. What is the maximum permissible value of P based on these stress limits?

A 36 kN B 45 kN C 60 kN D 75 kN

Question 21 ప్రశ్న 21

A steel bar and an aluminium bar have equal lengths and equal cross-sectional areas and carry the same tensile load. Take Esteel = 200 GPa and Ealuminium = 70 GPa. What is the ratio of aluminium elongation to steel elongation?

A 0.35 B 1.00 C 2.00 D 2.86

Question 22 ప్రశ్న 22

A three-segment bar ABCD is fixed at A. Loads of 20 kN to the right at B, 50 kN to the left at C and 100 kN to the right at D are applied. Segment AB has L = 600 mm, A = 350 mm² and E = 200 GPa; BC has L = 700 mm, A = 500 mm² and E = 70 GPa; CD has L = 800 mm, A = 400 mm² and E = 200 GPa. What is the displacement of D relative to A?

A 1.6 mm elongation B 2.0 mm elongation C 2.6 mm elongation D 3.2 mm elongation

Question 23 ప్రశ్న 23

Two segments connected in series carry the same tensile force. A steel segment has L = 1000 mm, A = 500 mm² and E = 200 GPa. An aluminium segment has L = 600 mm and E = 70 GPa. What aluminium area will make the elongations of the two segments equal?

A 420 mm² B 600 mm² C 700 mm² D 857 mm²

Question 24 ప్రశ్న 24

A stepped axial member experiences both tensile and compressive segment forces because of multiple applied axial loads. If the distance between its two end points is required to remain unchanged, which compatibility condition must be satisfied within the small-deformation linear-elastic model?

A The arithmetic sum of the magnitudes of all segment deformations must be zero. B Every segment must individually have zero stress. C The algebraic sum Σ(NiLi/AiEi) must be zero. D All segments must have identical cross-sectional areas.

Question 25 ప్రశ్న 25

Consider the following statements for a linearly elastic stepped bar subjected to concentrated axial loads:
1. The internal axial force in any segment can be determined by equilibrium of either portion obtained by cutting that segment.
2. Total axial deformation is the algebraic sum of the individual segment deformations.
3. A compressive deformation in one segment can partially or completely offset tensile elongation in another segment.
4. The internal axial force in every segment must equal the load applied at the free end even when additional concentrated loads act at intermediate points.

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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