A pretensioned rectangular concrete beam is 150 mm wide and 300 mm deep. Three straight tendons, each 50 mm² in area, are initially stressed to 1200 N/mm² and located 100 mm above the soffit. The modular ratio is 6. Find the prestressing-force loss in kN due only to elastic deformation of concrete, to one decimal place.
Total tendon area is $A_s=150$ mm², giving initial prestress $P=180000$ N. The tendon eccentricity is $e=150-100=50$ mm. Concrete area is 45000 mm² and $I=150(300)^3/12=337500000$ mm⁴. Stress at tendon level is $P/A+Pe^2/I=4+1.333=5.333$ N/mm². Elastic-shortening loss in steel stress is $6(5.333)=32$ N/mm². The force loss is $32(150)=4800$ N = 4.8 kN.
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