Post on 21-Feb-2023
Fall 2014 AE 5301-005/ME5390-005
Advanced Mechanics of Materials
HW Assignment # 1
Solution
Your 10-digit UTA ID (also known as 1000 number) has the following form:
1000 β XY β LMNP
where X, Y, L, M, N and P are the digits between 0 and 9. Find X, Y, L, M, N and P from your UTA ID to solve some of the following problems:
1. Consider the following stress matrix:
[π]= οΏ½π β 2 π 0π π + 1 00 0 0
οΏ½
Determine the components of the traction vector with respect to an area rotated ΞΈ about the z axis. Determine the components of stress transformed an angle ΞΈ about the same axis. Have you observed any relations between these two? 2. Determine the principal values and their orientations for the following stress matrix.
[π]= οΏ½π β 2 π ππ π + 1 0π 0 1
οΏ½
3. Under what circumstances is the following symmetric stress field in static
equilibrium? ππ₯π₯ = 3π₯; ππ¦π¦ = 4π¦; ππ₯π¦ = π΄π₯ + π΅π¦ (all in MPa)
Find stress vectors on the four sides of the rectangular body with side along x = 2 m and along y = 0.5 m. Using stress-strain relations for plane-stress, determine the deformed shape.
4. A cube of steel of slide 250 mm is loaded with a uniformly distributed pressure of
200 MPa on the four faces having normal in the x and y directions. Rigid constraints limit the total deformation of the cube in the z directions to 0.05 mm. Determine the normal stress, if any, which develops in the z direction.