Compression. 3 Rods

SOM-3Rods-EN

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Calculate separately three bars made of different materials, each subjected to a compressive force of 400 kN:
- a concrete bar with a square cross-section
- a wooden bar with a circular cross-section
- a steel bar with a rectangular cross-section.
The length of each bar is 1.4 m.

Material	Allowable stress, MPa	Young's modulus, GPa (1 GPa = 1000 MPa)	Density, t/m³	Material price
Concrete	6	21	2.4	160 $/m³
Wood	11	10	0.8	800 $/m³
Steel	185	200	7.85	1500 $/t

*The values in the table are given specifically for this problem. Actual material properties vary depending on the steel grade, wood species, and concrete class.

Concrete bar calculation

Required minimum cross-sectional area, cm²

Cross-section dimension, cm

Shortening of the bar, mm

Mass of the bar, kg

Material cost, $

Wooden bar calculation

Required minimum cross-sectional area, cm²

Cross-section diameter, cm

Shortening of the bar, mm

Mass of the bar, kg

Material cost, $

Steel bar calculation

Required minimum cross-sectional area, cm²

Cross-section dimension a, cm

Shortening of the bar, mm

Mass of the bar, kg

Material cost, $

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About this task

This task compares the behaviour of concrete, wooden, and steel bars subjected to the same axial compressive load. Students determine the required cross-sectional area for each material based on allowable stress, calculate the corresponding dimensions, evaluate elastic shortening using Young's modulus, and estimate both the mass and material cost of each bar. The exercise highlights the influence of material properties on structural performance and develops practical skills in axial compression analysis, material selection, and engineering design decisions. It is suitable for introductory strength of materials and mechanics of materials courses.