Question

10. A steel bvar, area 625 mm2, is embedded in a block of concrete 10o 100 mm. The length of both the steel bar and concrete block is 300 mm (see Fig. 14). Assuming a value of 210 kN/mm2 for Young s Modulus for the steel, and 14 kN/mm2 for the concrete, determine the load carried by the steel, and the load carried by the concrete, if the combined section subject to a compressive load of 5 kN. Assume that there is no slip between the steel and concrete fi.e. the strain in both materials is is equal and that the load is applied over the entire cross section. 5kN 100 mm 100 mm 300 mm g. 14

A steel bar , area 625 mm^2 , is embedded in block of concrete 100mm × 100mm. The length of both the steel bar and concrete block is 300 mm . Assuming a value of 210kN/mm^2 for young modulus for steel and 14 kN/mm^2 for concrete , determine the load carried by the steel and the load carried by the concrete , if the combined section is subject to a compressive load of 5kn . assume that there os no slip between the steel and concrete

Answer 1

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Area of block = 100 times 100 Area of steel bar (A_st) = 625 mm^2 So, Area of concrete (A_c) = 100 times 100 - 625 = 9357 mm^2 Length of block = 300 mm Young modulus for steel (E_s) = 210 kN/mm^2 for concrete (E_c) = 14 kN/mm^2 Total applied (p) = 5 kN So, total Load = Load carried by concrete + Load carried by steel p = p_c + p_s As there is no slip b/w them strain will be same. So, strain = stress/E so sigma_s/E_s = sigma_c/E_c p_s/A_s times E_s = p_c/A_c times E_c p_s/625 times 210 = p_c/9375 times 14 p_s/p_c = 1 p_s = p_c So, both carries same load So, load carried by steel = p/2 = 2.5 kN and Load carried by concrete = p/2 = 2.5 kN

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