Video from my You tube channel

Subscribe to My You tube channel

Example: Change in length for a bar with continuously varying load or dimensions

A tapered bar AB of solid circular cross-section and length L (Fig. 1-a) is supported at end B and subjected to a tensile load P at the free end A. The diameters of the bar at ends A and B are dA and dB, respectively. Determine the elongation of the bar due to the load P, assuming that the angle of taper is small.

Figure 1








in this example force is constant through the whole length of the tapered, to obtain the elongation we should derive an expression for area, therefore we should set an origin for our coordination x. to simplify the problem we will extend the side of the bar until it intersect at point O, we set the origin of our coordination system at point O.

From triangle similarity

 dA/LA=dB/LB

For d(X)

 d(x)/X=dA/LA

  d(X)=dA*X/LA

A(X)=π*(diameter^2)/4
diameter for the bar=dx
A(X)=π*((dA*X/LA)^2)/4
A(X)=π*((dA^2*X^2)/LA^2)/4









dδ=(N(X)*dx)/(A(X)*EA)



dδ=(4*P*LA^2dx)/(EA*π*dA^2*X^2)




 
δ



δ


 δ
for simplification





substitute  this to δ



we substitute LA/LB=dA/dB see previous equation


δ


Comments

Popular posts from this blog

Field density test-sand cone method

Zero force member for truss

Example 1: Design of one-way slab

Determinate and indeterminate structure

Pile cap

Tributary area(Loading)

Flakiness Index and Elongation Index of Coarse Aggregates

Types of structure

Strength reduction factor ∅

Heavyweight concrete