A square steel plate is 8.00 cm on a side and 0.800 cm thick. Assume that the pl

Question

A square steel plate is 8.00 cm on a side and 0.800 cm thick. Assume that the plate is oriented with the square faces horizontal to the ground. As shown in (Figure 1) a force of magnitude 1.00×106 N is applied to both the top and bottom surfaces of the plate (the square sides). Each of the forces is applied in a direction parallel to the surface they are exerted on, and they point in opposite directions. Find the shear strain caused by these forces. Note that the shear modulus of steel in pascals is 7.50×1010 Pa . Express the strain numerically to three significant figures. Part B Find the displacement ?x in centimeters. Express your answer in centimeters to three significant figures.

Explanation / Answer

given , square plate is of size 8.0cm and thickness is of 0.8cm

so, the plate is horizontal to ground and a force of magnitude 1.00*10^5N is applied to the top and bottom square face of the plate, parallel to the side, so shear stress occurs,

shear stress on both faces of the plate = force/(area perpendicular to the force)

= 1*10^5 / (8.0*0.8*10^(-4))

= 156.25*10^6 pa

so, A) shear strain (parellel to the side) = shear stress/ shear modulus of steel

= 156.25*10^6 pa / (7.50*10^10) Pa

= 0.00208

B) displacement (delx) = X( size of the square plate) * shear strain

= (8 * 0.00208 ) cm

= 0.01664 cm

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.