2-5.  Six reinforcing rods, each with a diamter of mm, are embedded in a concrete piece with a diameter of mm. If the piece is subjected to an axial force of  kN, determine the normal stress in the concrete and in the rods. The constantsGPa and GPa are given.

Fig. 2.5

Solution

Find the area of the rod and of the concrete.

 m²

 m²

Develop the equilibrium equation for the piece.

Next, develop a compatability equation.

To solve for the normal stress in the rods, combine the equilibruim equation and the compatability equation to derive an equation for  in terms of P.

Solve for the normal stress in the rods.

= 95.1 MPa

= 0.00128 MPa

Thus

 MPa                                                   Ans.

To solve for the normal stress in the concrete, combine the equilibrium equation and the compatability equation to derive an equation for  in terms of P.

Solve for the normal stress in the concrete.

= 11.3 MPa

= 0.000153 MPa

Thus

 MPa                                     Ans.