Test 4 - Compound Bars

Question 1 ప్రశ్న 1

A compound bar consists of two different materials of equal length, perfectly connected so that they deform together under an axial load. Which pair of conditions forms the basic basis for determining the load shared by the two materials?

A Equal stresses in both materials and zero total load B Equilibrium of the total axial load and compatibility of axial deformation C Equal cross-sectional areas and equal Young's moduli D Equal loads in both materials irrespective of their properties

Question 2 ప్రశ్న 2

A steel bar and an aluminium bar of equal length are rigidly connected in parallel between common end plates and remain elastic. If their Young's moduli are 200 GPa and 80 GPa respectively, what is the ratio of steel stress to aluminium stress?

A 1.25 B 2.00 C 2.50 D 4.00

Question 3 ప్రశ్న 3

A steel member of area 600 mm² and E = 200 GPa and a brass member of area 900 mm² and E = 100 GPa are of equal length and rigidly connected in parallel. If they jointly carry an axial tensile load of 180 kN, what loads are carried approximately by the steel and brass members?

A Steel 90.0 kN and brass 90.0 kN B Steel 102.86 kN and brass 77.14 kN C Steel 120.0 kN and brass 60.0 kN D Steel 77.14 kN and brass 102.86 kN

Question 4 ప్రశ్న 4

A compound member 1500 mm long consists of a steel component of area 500 mm² and E = 200 GPa together with a brass component of area 700 mm² and E = 100 GPa. The equal-length components are rigidly connected and jointly carry 170 kN tension. What is the elongation of the compound member?

A 0.75 mm B 1.00 mm C 1.50 mm D 2.00 mm

Question 5 ప్రశ్న 5

A steel component of area 400 mm² and E = 200 GPa and an aluminium component of area 600 mm² and E = 70 GPa are perfectly bonded over the same length. If the compound member carries 122 kN tension, what are the stresses in steel and aluminium?

A Steel 122 MPa and aluminium 122 MPa B Steel 200 MPa and aluminium 70 MPa C Steel 175 MPa and aluminium 100 MPa D Steel 244 MPa and aluminium 42 MPa

Question 6 ప్రశ్న 6

A compound member consists of a steel element having A = 500 mm² and E = 200 GPa and a brass element having A = 800 mm² and E = 100 GPa, both of equal length and connected to deform together. What is the equivalent axial rigidity ΣAE of the compound section?

A 100 × 10^6 N B 140 × 10^6 N C 180 × 10^6 N D 260 × 10^6 N

Question 7 ప్రశ్న 7

Two materials of equal length are perfectly bonded to form a compound bar and remain linearly elastic. Their Young's moduli are E1 = 200 GPa and E2 = 80 GPa. If the common longitudinal strain is ε, which stress relationship is correct?

A σ1 = σ2 B σ1 = 0.4σ2 C σ1 = 2.5σ2 D σ1 = 4σ2

Question 8 ప్రశ్న 8

A steel member of area 300 mm² and E = 200 GPa is to be connected in parallel with an aluminium member of E = 75 GPa and the same length. What aluminium area is required if the two members are to carry equal axial loads?

A 450 mm² B 600 mm² C 750 mm² D 800 mm²

Question 9 ప్రశ్న 9

Three equal-length members are rigidly connected in parallel: steel with A = 400 mm² and E = 200 GPa, brass with A = 600 mm² and E = 100 GPa, and aluminium with A = 800 mm² and E = 75 GPa. If the total tensile load is 200 kN, what load is carried by the steel member?

A 60 kN B 80 kN C 100 kN D 120 kN

Question 10 ప్రశ్న 10

Two axial rods are attached to the same rigid loading plate, while their opposite ends are fixed to separate supports so that their original lengths may differ. The steel rod has L = 1000 mm, A = 500 mm² and E = 200 GPa, while the aluminium rod has L = 500 mm, A = 500 mm² and E = 70 GPa. If a 170 kN tensile load causes the rigid plate to translate axially without rotation, what are the plate displacement and respective rod forces?

A Displacement 1.0 mm; steel 100 kN and aluminium 70 kN B Displacement 1.0 mm; steel 85 kN and aluminium 85 kN C Displacement 2.0 mm; steel 100 kN and aluminium 70 kN D Displacement 0.5 mm; steel 120 kN and aluminium 50 kN

Question 11 ప్రశ్న 11

Two elastic rods of different original lengths have one end attached to the same rigid loading plate and their opposite ends fixed to separate supports. If the plate translates axially without rotation and the rods remain aligned with the loading direction, which compatibility statement is generally correct?

A Their axial stresses must be equal. B Their axial strains must be equal even when their lengths differ. C Their changes in length are equal, while their strains may differ. D Their axial forces must be equal irrespective of stiffness.

Question 12 ప్రశ్న 12

A steel rod and an aluminium rod are attached to the same rigid loading plate, with their opposite ends fixed to separate supports. The steel rod has L = 1200 mm, A = 400 mm² and E = 200 GPa, while the aluminium rod has L = 800 mm, A = 600 mm² and E = 70 GPa. If the rigid plate translates axially by 0.60 mm without rotation, what total axial force is required?

A 40.0 kN B 55.5 kN C 71.5 kN D 83.0 kN

Question 13 ప్రశ్న 13

Consider the following statements about an equal-length, perfectly bonded compound bar under concentric axial loading:
1. The constituent materials undergo the same longitudinal strain.
2. The total load equals the sum of the loads carried by the constituents.
3. The stresses in all constituent materials must be equal.
4. The load carried by a constituent is proportional to AE when all constituents have the same strain.

Which statements are correct?

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

Question 14 ప్రశ్న 14

Match the compound-member concept with the appropriate relationship:
1. Axial equilibrium
2. Equal-length compatibility
3. Load carried by constituent i
4. Equivalent axial rigidity

P. Pi = AiEiε
Q. ΣPi = P
R. ΣAiEi
S. ε1 = ε2 = ...

Which matching is correct?

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

Question 15 ప్రశ్న 15

A fixed total cross-sectional area is available for an equal-length compound member made from two linearly elastic materials. If some area is transferred from the material having the higher Young's modulus to the material having the lower Young's modulus, with total area unchanged, what happens to the equivalent axial rigidity ΣAE?

A It necessarily increases. B It decreases. C It remains unchanged because total area is unchanged. D It becomes zero.

Question 16 ప్రశ్న 16

A steel member of area 300 mm² and E = 200 GPa is connected in parallel with an aluminium member of E = 80 GPa and the same length. If the steel member is required to carry exactly 60 percent of the total axial load, what aluminium area is required?

A 300 mm² B 400 mm² C 500 mm² D 750 mm²

Question 17 ప్రశ్న 17

A steel member with A = 500 mm², E = 200 GPa and allowable tensile stress 160 MPa is rigidly connected in parallel with an equal-length aluminium member having A = 800 mm², E = 70 GPa and allowable tensile stress 90 MPa. What is the maximum total tensile load the compound member can carry while both stress limits are satisfied?

A 112.0 kN B 124.8 kN C 152.0 kN D 176.0 kN

Question 18 ప్రశ్న 18

An equal-length steel-brass compound bar has steel area 400 mm², Es = 200 GPa and allowable steel stress 150 MPa, while the brass area is 600 mm², Eb = 100 GPa and allowable brass stress 100 MPa. What maximum total tensile load is permitted?

A 90 kN B 105 kN C 120 kN D 140 kN

Question 19 ప్రశ్న 19

An equal-length composite member consists of two parallel components whose axial rigidities AE are 80 × 10^6 N and 40 × 10^6 N. If the second component is removed and the same total axial load is then carried only by the first component, by what factor does the elastic deformation increase?

A 1.25 B 1.50 C 2.00 D 3.00

Question 20 ప్రశ్న 20

A perfectly bonded equal-length steel-brass compound member experiences a measured tensile strain of 0.0006. Steel has A = 300 mm² and E = 200 GPa, while brass has A = 500 mm² and E = 100 GPa. What total tensile load is acting on the compound member?

A 54 kN B 60 kN C 66 kN D 72 kN

Question 21 ప్రశ్న 21

In an equal-length perfectly bonded two-material compound bar under axial loading, can the stresses in the two materials generally be made equal merely by changing their cross-sectional areas while retaining different Young's moduli?

A Yes, because stress is always inversely proportional to area in a compound member. B Yes, provided the total area is unchanged. C No; under equal-strain compatibility their stress ratio is determined by the ratio of their Young's moduli. D No; because both constituent stresses must always be zero.

Question 22 ప్రశ్న 22

For an equal-length, perfectly bonded compound bar having total area At = ΣAi and common axial strain, which expression gives the equivalent Young's modulus Eeq of a homogeneous bar having the same total area and the same axial rigidity?

A Eeq = ΣEi B Eeq = At/Σ(AiEi) C Eeq = Σ(AiEi)/At D Eeq = Σ(Ai/Ei)

Question 23 ప్రశ్న 23

A perfectly bonded compound bar contains 400 mm² of steel with E = 200 GPa and 600 mm² of aluminium with E = 70 GPa. What is the equivalent Young's modulus of a homogeneous bar having the same total cross-sectional area and axial rigidity?

A 100 GPa B 122 GPa C 135 GPa D 148 GPa

Question 24 ప్రశ్న 24

An equal-length three-material compound member 1200 mm long consists of steel with A = 300 mm² and E = 200 GPa, brass with A = 500 mm² and E = 100 GPa, and aluminium with A = 1200 mm² and E = 75 GPa. If the member carries 200 kN tension, what is its total elongation?

A 0.60 mm B 1.00 mm C 1.20 mm D 2.00 mm

Question 25 ప్రశ్న 25

Consider the following statements about axially loaded compound members:
1. Equal-length constituents connected so that no relative axial slip occurs have equal longitudinal strain.
2. For such constituents in the linear-elastic range, their stresses are proportional to their Young's moduli.
3. Their loads are necessarily equal regardless of cross-sectional area and modulus.
4. Parallel members of unequal original lengths attached to a common rigid moving plate and fixed at their other ends can undergo the same end displacement while developing different axial strains.

Which statements are correct?

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

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