The rigid beam is supported by a pin at A and wires BD and CE.

If the load P on the beam causes the end C to be displaced 10 mm

downward, determine the normal strain developed in wires CE and

BD.

General guidance

Concepts and reason

Strain: When the alloy is stressed in specific direction the response of the system for this stress is strain. The deformation of an alloy in specified direction divided by the original length gives the strain the alloy.

The normal strain developed in wires is calculated by using the similar triangle rule.

Deformation is assumed to be linear as they are very small compared to the original length of the wire.

Fundamentals

Stress: A body offers some internal resistant force under the action of a load.

This internal resistant force per unit cross-sectional area is termed as stress.

The stress can be calculated by,

Here, the force applied on the material is P and the cross-sectional area on which the force acts is A.

The strain can be calculated by,

Here, the change in length of the material is and its original length is L.

Step-by-step

Step 1 of 4

Draw the deformation diagram.

Similar triangle rule: Two triangles are said to be similar if the corresponding angles are congruent and the corresponding sides are in proportion.

According to the similar triangle rule.

Calculate the deformed length.

Step 2 of 4

Calculate the change in length of the wire BD.

Here, is the change in length of the wire BD and is the change in length of the wire CE.

Substitute 10 mm for .

Using similarity of triangles, the expression to calculate change in length of the wire BD is derived. The change in length of the wire CE is given in the question as 10 mm. this value is substituted in the expression to get the value of the change in length of the wire BD as 4.3 mm.

Calculate the normal strain developed in the wire CE.

Step 3 of 4

Calculate the normal strain developed in the wire CE.

Substitute 10 mm for .

The normal strain is the ratio of the change in length to the original length. The original length is 4000 mm. The normal strain developed in the wire CE is then obtained to be 0.0025.

Calculate the normal strain developed in the wire BD.

Step 4 of 4

Calculate the normal strain developed in the wire BD.

Substitute 4.3 mm for .

Therefore, the normal strain developed in the wires CE and BD are and respectively.

The normal strain is the ratio of the change in length to the original length. The original length is 4000 mm. The normal strain developed in the wire BD is then obtained to be 0.00107.

Please note that strain has no units.

Answer

Therefore, the normal strain developed in the wires CE and BD are and respectively.

Answer only

Therefore, the normal strain developed in the wires CE and BD are and respectively.

P

SL E =

SL

4 m 3 m В А AL, |ALCE “СЕ D E

B D A E C a

_ У АС АЕ х

ALALE СЕ 3 7

AL BD

ALCE СЕ

ALCE СЕ

ALIRD10 7 BD

СЕ &ск 4000 СЕ

ALCE СЕ

10 ECE 4000 ECE = 0.0025 mm/mm

ALBD ED4000

AL BD

4.3 E BD 4000 RD 0.00107 mm/mm

0.0025mm /mm

0.00107 mm /mm

0.0025 mm/mm

0.00107 mm/mm

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