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Thermal stresses, Bars subjected to tension and Compression
Compound bar: In certain application it is necessary to use a combination of elements or bars made from different materials, each material performing a different function. In over head electric cables or Transmission Lines for example it is often convenient to carry the current in a set of copper wires surrounding steel wires. The later being designed to support the weight of the cable over large spans. Such a combination of materials is generally termed compound bars.
Consider therefore, a compound bar consisting of n members, each having a different length and cross sectional area and each being of a different material. Let all member have a common extension ‘x' i.e. the load is positioned to produce the same extension in each member.
Where Fn is the force in the nth member and An and Ln are its cross - sectional area and length.
Let W be the total load, the total load carried will be the sum of all loads for all the members.
Therefore, each member carries a portion of the total load W proportional of EA / L value.
The above expression may be writen as if the length of each individual member in same then, we may write
Thus, the stress in member '1' may be determined as s1 = F1 / A1
hus, the stress in member '1' may be determined as s1 = F1 / A1
Determination of common extension of compound bars: In order to determine the common extension of a compound bar it is convenient to consider it as a single bar of an imaginary material with an equivalent or combined modulus Ec.
Assumption: Here it is necessary to assume that both the extension and original lengths of the individual members of the compound bar are the same, the strains in all members will than be equal.
Total load on compound bar = F1 + F2+ F3 +………+ Fn where F1 , F 2 ,….,etc are the loads in members 1,2 etc
But force = stress . area,therefore s (A 1 + A 2 + ……+ A n ) = s1 A1 + s2 A2 + ........+sn An
Where s is
Compound bar: In certain application it is necessary to use a combination of elements or bars made from different materials, each material performing a different function. In over head electric cables or Transmission Lines for example it is often convenient to carry the current in a set of copper wires surrounding steel wires. The later being designed to support the weight of the cable over large spans. Such a combination of materials is generally termed compound bars.
Consider therefore, a compound bar consisting of n members, each having a different length and cross sectional area and each being of a different material. Let all member have a common extension ‘x' i.e. the load is positioned to produce the same extension in each member.
Where Fn is the force in the nth member and An and Ln are its cross - sectional area and length.
Let W be the total load, the total load carried will be the sum of all loads for all the members.
Therefore, each member carries a portion of the total load W proportional of EA / L value.
The above expression may be writen as if the length of each individual member in same then, we may write
Thus, the stress in member '1' may be determined as s1 = F1 / A1
hus, the stress in member '1' may be determined as s1 = F1 / A1
Determination of common extension of compound bars: In order to determine the common extension of a compound bar it is convenient to consider it as a single bar of an imaginary material with an equivalent or combined modulus Ec.
Assumption: Here it is necessary to assume that both the extension and original lengths of the individual members of the compound bar are the same, the strains in all members will than be equal.
Total load on compound bar = F1 + F2+ F3 +………+ Fn where F1 , F 2 ,….,etc are the loads in members 1,2 etc
But force = stress . area,therefore s (A 1 + A 2 + ……+ A n ) = s1 A1 + s2 A2 + ........+sn An
Where s is