Series rods share force, not stress

Two 1.0 m rods in series fit between rigid supports without initial stress. Their cross-sectional areas are 10 mm² and 20 mm²; their α values are 10 × 10⁻⁶ and 20 × 10⁻⁶ K⁻¹ respectively. Both have Y = 100 GPa and warm by 30 K. Exclude buckling and yielding.

What is the common compressive force magnitude?

Organize the givens & assumptions

L1 = L2 = 1 m
A1 = 10 mm²; A2 = 20 mm²
α1 = 10 × 10⁻⁶; α2 = 20 × 10⁻⁶ K⁻¹
Y1 = Y2 = 100 GPa
Rise = 30 K

Uniform temperatures and the stated expansion coefficients; small thermal strains and first-order expansion unless a retained ratio is explicitly requested. Free expansion except for the named axial constraints. Constrained rods remain straight and linearly elastic; no buckling, yielding or moving supports.

A $600\ \mathrm N$
B $900\ \mathrm N$
C $450\ \mathrm N$
D $1200\ \mathrm N$

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