# The elastic strip with a cutout is of length L, width b, and thickness t. Derive the expression for the elongation of the strip caused by the axial load P.

Question-AnswerCategory: Strength of MaterialsThe elastic strip with a cutout is of length L, width b, and thickness t. Derive the expression for the elongation of the strip caused by the axial load P.

The elastic strip with a cutout is of length L, width b, and thickness t. Derive the expression for the elongation of the strip caused by the axial load P.

Mazurek Gravity answered 11 months ago

Step No: 1

Draw the free body diagram of elastic strip of uncut portion.

Step No: 2

Calculate the elongation of elastic strip using the relation.

Here, is elongation of uncut portion of elastic strip,  is axial tensile load applied on elastic strip, length of elastic strip of uncut portion, is young’s modulus of steel wire and cross section area of elastic strip of uncut portion.
Substitute  for and for
.

Here, is width of strip and  is thickness of strip.

Step No: 3

Draw the free body diagram of cut portion of elastic strip.

Step No: 4

Calculate elongation of cut portion of elastic strip using the relation.

Here,  is elongation of cut portion of strip, is axial tensile load applied on elastic strip, length of cut portion of elastic strip, is young’s modulus of steel wire and cross section area of elastic strip of cut portion.
Substitute  for and for
.

Here, is width of strip and  is thickness of strip.

Step No: 5

Derive the expression for total elongation of elastic strip for using the relation.

Here, is total elongation of elastic strip, is elongation of uncut portion of strip and  is elongation of uncut part of strip.
Substitute for andfor.

Therefore, the expression for total elongation of elastic strip is