Tutorial 1 Problem 1 (ENGR5004)

Tutorial 1 Problem 1Exercise sheetCurrent spec2:210 min

ENGR5004 Statics Tutorial Sheet 1, Problem 1 official answers

A rod of length $L$ , cross-sectional area $A_1$ , and modulus of elasticity $E_1$ has been placed inside a tube of the same length $L$ , but of cross-sectional area $A_2$ and modulus of elasticity $E_2$ . A force $P$ is applied on a rigid plate attached to both tube and rod, as shown in the sketch below. Determine:

HINT: deformation of tube and rod is constrained to be the same.

Rod (A1, E1) inside a tube (A2, E2), both fixed to the wall at the left and to a rigid end plate at the right; force P pushes the plate towards the wall.

Formulas you may need

Axial deformation: $\delta = \dfrac{PL}{AE}$ (learn this)
Equilibrium of the end plate: $P_1 + P_2 = P$ (learn this: free-body diagram)
Compatibility (rigid plate): $\delta_1 = \delta_2$ (learn this)

(a)
the horizontal displacement $\delta$ of the rigid plate as a function of $P$ , $L$ , $A_1$ , $A_2$ , $E_1$ and $E_2$ ;
(b)
the fixed support reactions acting on the rod ( $P_1$ ) and tube ( $P_2$ ) when $E_1 = E_2$ ;
(c)
the fixed support reactions acting on the rod ( $P_1$ ) and tube ( $P_2$ ) when $E_1 = 2E_2$ ;