Solid Mechanics Stiffness Question

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SUMMARY

The discussion centers on calculating the number of steel rods required to achieve a minimum axial stiffness of 2000 kN/mm for a concrete post measuring 0.5m in height and 100mm in diameter, reinforced with 10mm diameter steel rods. The formula derived for the number of rods is n = (4D²)/(5d²), which results in an incorrect value of 80. Participants highlight the need for clarity regarding the units of stiffness (k) and the forces involved in the equation k = F/(EA), indicating potential errors in the initial calculations.

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  • Understanding of axial stiffness in solid mechanics
  • Familiarity with the properties of concrete and steel materials
  • Knowledge of basic structural engineering equations
  • Proficiency in unit analysis for stiffness calculations
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Homework Statement



A 0.5m high and 100mm diameter post is to be made from concrete reinforced by 10mm diameter steel rods. How many steel rods should be used if the axial stiffness of the post is to be at least 2000kN/mm?

Homework Equations



n = number of steel rods
D = diamater of the post
d = Diameter of the steel rods

A Concrete= [tex]\stackrel{piD 2}{4}[/tex] - n [tex]\stackrel{pid 2}{4}[/tex]
A Steel = n [tex]\stackrel{pid 2}{4}[/tex]k (Stiffness) = F/(EA)

The Attempt at a Solution



Strain compatibility is assumed
[tex]\frac{E SteelA Steel}{L}[/tex] = [tex]\frac{E ConcreteA Concreete}{L}[/tex]

Substitute in Areas, and cancel where possible, I am left with n = [tex]\frac{4D<sup>2</sup>}{5d<sup>2</sup>}[/tex] which = 80, which is not right but i am struggling to see what I have done wrong.
 
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In your equ k=F/EA, what are the units of k on the LHS and what are the units of F/EA on the RHS? Isn't there something missing?
 

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