A square bar of 25 mm side is held between two rigid plates and loaded

1.	A square bar of 25 mm side is held between two rigid plates and loaded by an axial pull equal to 300 kN as shown in figure. Determine the reactions at end A and C and elongation of the portion AB. Take E = 2 × 105N/mm2 .
Answer» Cross section area of the bar A = 25 × 25 mm² Since the bar is held between rigid support at the ends, the following observations need to be made: Portion AB will be subjected to tension and portion BC will be under compression Since each ends are fixed and rigid and therefore total Elongation; \(\delta\)L_ab – \(\delta\)L_bc = 0; Elongation in portion AB equals shortening in portion BC. i.e., \(\delta\)L_ab = \(\delta\)L_bc Sum of reactions equals the applied axial pull i.e., P = R_a + R_c Apply second condition, we get [P_ab × L_ab]/A_ab.E = [P_bc × L_bc]/A_bc.E (R_a × 400)/(625 × 2 × 10⁵ ) = (R_c × 250)/(625 × 2 × 10⁵ ) R_c= 1.6R_a (i) Now apply third condition i.e., P = R_a + R_c 300 × 10³ = R_a + 1.6 R_a R_a = 1.154 × 10⁵ N; R_c = 1.846 × 10⁵ N

A square bar of 25 mm side is held between two rigid plates and loaded by an axial pull equal to 300 kN as shown in figure. Determine the reactions at end A and C and elongation of the portion AB. Take E = 2 × 105N/mm2 .

Answer»

Cross section area of the bar A = 25 × 25 mm²

Since the bar is held between rigid support at the ends, the following observations need to be made:

Portion AB will be subjected to tension and portion BC will be under compression
Since each ends are fixed and rigid and therefore total Elongation;

\(\delta\)L_ab – \(\delta\)L_bc = 0; Elongation in portion AB equals shortening in portion BC. i.e.,

\(\delta\)L_ab = \(\delta\)L_bc

Sum of reactions equals the applied axial pull i.e., P = R_a + R_c

Apply second condition, we get

[P_ab × L_ab]/A_ab.E = [P_bc × L_bc]/A_bc.E

(R_a × 400)/(625 × 2 × 10⁵ ) = (R_c × 250)/(625 × 2 × 10⁵ )

R_c= 1.6R_a (i)

Now apply third condition i.e., P = R_a + R_c

300 × 10³ = R_a + 1.6 R_a

R_a = 1.154 × 10⁵ N; R_c = 1.846 × 10⁵ N