Analysis Beam on Elastic FoundationDescripción completa
StatisticsFull description
Contains all the assignments for CSE UoPFull description
This is a broad outlook on solving assignments.
Full description
Some problems from wileyFull description
BBS Entrance Questions
Full description
Operators and Assignments in Java, a very much confodent appoach..Full description
Assignments
1.
Describe Describe the similari similarities ties and the differ difference encess between between a plane stress stress problem and and a plane strain strain problem. Answer
2. The state of stress in a rectangular plate under uniform biaxial loading, as shown in the following figure, is found to be
σ ij
X = 0 0
0
0
Y
0
0
0
Determine the traction vector and the normal and shearing stresses on the oblique plane .
A!"#$
%. &or the case of pure shear, the stress matrix is given b '
0 τ σ ij = τ 0 0 0 where
τ
0
0 0
is a given constant. Determine the principal stresses and directions.
A!"#$
(. A two)dimensional problem of a rectangular bar stretched b' uniform end loadings results in the
following constant strain field* ε x
= C 1 , ε y = −C 2 and γ xy = 0 ,where
+1 and +2 are constants.
Assuming the field depends onl' on x and ', integrate the strain)displacement relations to determine the displacement components and identif' an' rigid)bod' motion terms.
% % 5. Show that the following strain eld: ε x = Ay , ε y = Ax and γ xy = 2 Bxy x + y -
gives continuous, single-valued displacements in a simply connected region only if the constants are related by A =
2 %
B
6. #xpress all boundar' conditions for each of the problems illustrated in the following figure.
Answer
. aint)/enants principle allows particular boundar' conditions to be replaced b' their equivalent resultant. &or problems b-,d-, and f- in exercise , the support boundaries that had fixed displacement conditions can be modified to specif' the staticall' equivalent reaction loadings. Develop the resultant loadings over the fixed boundaries for each of these cases. Answer
. 3iven the following stress state* σ x
= C y 2 + µ x 2 − y2 -
,
σ y = C x 2 + µ y 2 − x2 - ,
σ z = C µ x 2 + y 2 - , τ xy = −2C µ xy , τ yz = τ zx = 0 Discuss wh' this stress state ma' not be a solution of a problem in elasticit'.
4. #xplicitl' show that the fourth order pol'nomial Air' stress function ax satisf' the bi)harmonic equation unless %a + b + %c
10. #xamine that the function
(
+ bx 2 y 2 + cy ( will not
= 0.
φ = a x ( − y ( - a50- ma' be used as stress function. Derive the
stress components and determine the surface forces acting on the edges of the rectangular plate shown below 6od' forces are not involved-. 2 7 h
O
2 7 h
l 72
l 72
y
1
x
11. A beam, as shown in the figure, is sub8ected to pure bending in a plane stress state. The solution to the problem in terms of Air' stress function is given b' ϕ = ay . 1- #xpress the %
constant a in terms of the applied bending moment 9. 2- &ind the expressions for the stresses. 2&ind the expressions for the strains. 2- &ind the expressions for the displacements. y t h
x
12 A thin square plate has in it stresses σ x
= Cy and σ y = Cx ,
stresses τ xy . Determine the stresses and displacements.
and possibl' some shearing
y b
b
x
1%. The cantilever beam shown in the figure is sub8ected to distributed shearing forces with resultant force F : on the right face. Determine the stresses and displacements of the beam without considering the self weight. ;sing plane stress theor' and thic
2 7
x
h
2 7 h
F : l y
1
1(. Through a shrin<)fit process, a rigid solid c'linder of radius r 1 + δ is to be inserted into the hollow c'linder of inner radius r 1 and outer radius r 2 as shown in the following figure-. This process creates a displacement boundar' condition ur r1 - = δ . The outer surface of the hollow c'linder is to remain stress free. Assuming plane strain conditions, determine the resulting stress field within the c'linder r1
< r < r 2 -.
1=. A long composite c'linder is sub8ected to the external pressure loading as shown. Assuming ideali>ed perfect bonding between the materials, the normal stress and displacement will be continuous across the interface r displacement fields in each material.
