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MECHANICSOFSOLIDSI

Prof. Bhanuprakash Tallapragada

Dept. of Marine Engineering

Andhra UniversityVisakhapatnam 530003

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The shelf is bending under the weight of those books, and its

resting on the brackets at the ends. In Mechanics of Materials I can

represent this shelf approximately as a beam with simple supports.

I can approximate the books as applying a uniformly distributed

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I could make the shelf shorter, or maybe

might need some more analysis to see how

much that helps

I could use a stiffer material steel or aluminium, or a carbon reinforcedcomposite might be a little overkill for a bookshelf in my apartment . . . The

thickness of the shelf has much more effect on the resistance to bending than

does its width . . . So it could help a lot to use a thicker board

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Or I could ut a much thicker reinforcin

strip in the front . . . That should help . . .I wonder by how much . . .

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Why Study Mechanics of Materials?

1. Account for deformation and the potential for failure when

Forces acting on designed artifacts can be significant.

.

All bodies deform under applied forces, and they can fail if the forces are

sufficiently large.

Mechanics of Materials addresses two prime questions:

How much does a bod deform when sub ected to forces?

When will forces applied to a body be large enough to cause the body to

Deformation and failure depend on the forces and on the bodys material,

, .

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2. Inmostsituations,trytoavoidfailureandkeepdeformationswithinacceptablelimits.

Usually, the structure or system must remain intact even when subjected to forces. If we knowthe forces under which failure would occur, we can design to avoid failure. Further, a system

often needs to remain close to its original shape to function properly. If we can quantify

e orma ons, we can es gn e sys em o avo un es ra y arge e orma ons.

This com uterized weldin

system functions properly only if

the deflections of its track are

very small.

still be intact, it could be

viewed as having failed if

there is a permanent

A crack in a structure, such as this support

column, is a type of failure. This crack may

be repairable. A structure that fractures

.

that has deformed this

much is unlikely to be

useful.

unacceptable.

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3. Deformationisdesirableinsomesituationswhereitdependspredictablyon

theforces.

Some products must deform to carry out their function. They are designed to have a

desired relation between the deformation and the acting forces.

1. Such products include pole vaults that flex to temporarily store energy that later

propels the polevaulter.

2. mountings that accommodate motions of helicopter blades

3. support springs that allow for deflection of structural members.

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4.Occasionally,failureisdesirable,ifitoccursatareproduciblelevelofload

oug suc c rcums ances are rare, we some mes e era e y wan a ure o occurwhen loads reach a predetermined level. In expensive equipment, failure can be

. , ,

at a consistent force that is safely less than the main components can tolerate. For the

,

fuse. Just as an old fashioned electric fuse breaks when the current is too high, the pins in

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1.2HowMechanicsofMaterialsPredictsDeformationandFailure

.

With very general principles, we can consider bodies with a wide range of geometries and

materials, which are subjected to many types of loads.

Mechanics of Materials introduces these principles and applies them to bodies and

loadings that can be analyzed with relatively simple mathematics.. epara e ou e e ec s o ma er a an geome ry y v ew ng a o y as compose o

many tiny elements.

1. To predict deformation and failure, mechanics of materials relies on a critical insight: any

body can be viewed as an assemblage of tiny, in fact infinitesimal, cubic elements.

2. This insight allows us to separate out the effect of the bodys material from its shape.

. nce a t ny cu e s a stan ar s ape, t e re at ons etween t e cu e s e ormat on an

the forces on it depend only on the material, for example, the particular type of ceramic,

metal lastic or wood.

4. These relations can be measured and described for a given material, and they are relevant

to a body of any shape and size composed of that material.

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2. Relate forces and deformations at the

element level with those at the level of the

1. Mechanics of materials defines stress and

strain to describe force and deformation at the

level of an elemental cube.. o eterm ne a o y s overa e ormat on an

potential for failure, we combine

a the materials ecific stressstrain relations

for a cubic element,

b) equilibrium relations between forces on the

body as a whole and the forces on its elements,

and

c geome r c re a ons e ween e orma ons o

the whole body and of its elements.

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3. Recognize that loaded bodies often deform in simple patterns, namely,

stretching, twisting, or bending.

1. Engineers deal with deformation and failure in structures having a wide variety of

shapes, materials, and loadings.

. owever, n mec an cs o ma er a s, we s u y e orma on an a ure pr mar y

for simple patterns of deformation: stretching, twisting, or bending.

. or eac pattern, t e overa oa ng s escr e y equa an oppos te orces or

moments at the two ends.

4. The overall deformation is described by a single parameter: how much the body

s re c es, w s s, or en s.

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4. Study deflection and failure for each pattern individually, and then how they

combine. In mechanics of materials, we learn how the forces and deformations

vary from one cubic element to another for each deformation pattern.

1. With that information, we interrelate the overall load and deformation for that

pattern, and we find the load at which failure will occur.

2. As a byproduct, we gain insight into how the bodys geometry (length and cross

section) and the bodys material independently affect the overall deformation and

failure.3. Faced with applications that appear complex, we must also learn to detect the

presence of these simple deformation patterns, alone or, often, in combination.

4. We typically analyze the deformations and stresses in each pattern and then

com ne t em appropr ate y to n t e tota e ormat on an to eterm ne

failure will occur.