11. Concrete is a ceramic material that is strong in compression, but weak in tension. In...

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11. Concrete is a ceramic material that is strong in compression, but weak in tension. In construction, concrete is often reinforced using steel rods. We can model reinforced concrete as a continuous-fibre composite. Assume a tensile strength for concrete of 2 MPa, modulus of 20 GPa, and compressive strength of 20 MPa. Assume a modulus for steel of 200 GPa, and yield strength of 500 MPa. a. A 300 x 300 mm cross-sectional concrete beam with a length of 2 m is placed under a tensile stress. Show that the maximum force this beam would be expected to withstand is 180 kN. b. Assume that reinforced concrete is produced using steel rod with a diameter of 20 mm. Twenty of these rods are used to reinforced the beam above. i. What is the volume fraction of steel in the composite? ii. What is the expected modulus of the composite? iii. The same force from part (a) is applied to the composite. Calculate the forces within the steel reinforcing (fibres) and within the concrete (matrix). iv. The composite is being stretched longitudinally, and iso-strain conditions will apply. At what strain is the concrete expected to break? At what strain is the steel expected to yield? Use your answers to deduce the failure strain for the composite and what will happen under that loading v. Using your answer to parts (ii) and (iv), what force can the reinforced concrete beam hold without failing? 11. Concrete is a ceramic material that is strong in compression, but weak in tension. In construction, concrete is often reinforced using steel rods. We can model reinforced concrete as a continuous-fibre composite. Assume a tensile strength for concrete of 2 MPa, modulus of 20 GPa, and compressive strength of 20 MPa. Assume a modulus for steel of 200 GPa, and yield strength of 500 MPa. a. A 300 x 300 mm cross-sectional concrete beam with a length of 2 m is placed under a tensile stress. Show that the maximum force this beam would be expected to withstand is 180 kN. b. Assume that reinforced concrete is produced using steel rod with a diameter of 20 mm. Twenty of these rods are used to reinforced the beam above. i. What is the volume fraction of steel in the composite? ii. What is the expected modulus of the composite? iii. The same force from part (a) is applied to the composite. Calculate the forces within the steel reinforcing (fibres) and within the concrete (matrix). iv. The composite is being stretched longitudinally, and iso-strain conditions will apply. At what strain is the concrete expected to break? At what strain is the steel expected to yield? Use your answers to deduce the failure strain for the composite and what will happen under that loading v. Using your answer to parts (ii) and (iv), what force can the reinforced concrete beam hold without failing?