now, in this section we’ll discuss about,

tension developed in a clamped wire. say we’re having, a metal wire which is clamped between

2 rigid supports. say, these are rigid supports. and the wire is just taut. almost zero tension

is considered. say if we increase the temperature, then obviously the wire will expand, and there’ll

be a sag in the wire. so we can say that a sag is developed if temperature is increased,

it expands. and the tension will still remain zero. but say if we decrease the temperature,

and if it is just taut, say its temperature is decreased by delta t. in this situation

the wire will have a tendency to contract due to, thermal contraction phenomena. its

just the reverse of, thermal expansion. in this situation say, we open the wire from

1 end, then what happens is, we can say, the wire will contract upto, this much of length,

say which is delta l. earlier it was l not, it’ll be contracted by a length delta l

and we can write, thermal contraction. in length, will be delta l, which can be written

as, alpha l not delta t, length is l not. here alpha is the coefficient of linear expansion

of this wire. in this situation, if it remains clamped at, the rigid support, in that case,

whichever length is contracted due to thermal contraction, will be the same compensated

by elastic expansion. or if you can assume, say, it is contracted, and if i hold this

end and pull it and tie it up again at the rigid support, we can say that a tension is

developed in it. so the tension developed will be f, and the wire is, elastically expanded,

and, again it is, clamped at the rigid support. so in this situation, this tension, we can

call it f, which is developed within the length of this wire. so we can find out very easily

the tension developed in the wire by using, the young modulus of this metal wire. as we

know, young’s modulus. of material, can very easily be related by strain and stress

developed in the material. like, young modu-lus can be written as, stress by strain. so in

this situation, stress can be written as, f upon, s. where s is the cross sectional

area of the wire, which is equal to s. so the stress developed in the wire due to, elastic

elongation is, f by s, because f is the tension developed due to elastic elongation. and a

strain can directly be written as, delta l by l not. or you must consider the initial

length to be l not minus delta l, which can be approximately taken as l not. so in this

situation, this tension in, wire, can be written as, y s, delta l by, l not. and delta l by

l not from here we can write as alpha delta t, so it can be written as, y s, alpha delta

t. so, due to fall in temperature, if temperature fall is, delta t. and due to fall in temperature

by delta t, we can write, tension in wire, is equal to, y s, alpha delta t. so just keep

this thing in your mind. this is also very important result, that is quite useful in

different kinds of numerical problems.