Question Problem 2.1E A simply supported unreinforced concrete test beam spanning 1.4 m is shown in the figure below. The beam is of rectangular cross-section (100 mm width by 150 mm overall depth). The beam failed when subjected to two point loads of 3 kN each, as shown in the figure. The beam was made of normal-density concrete. Determine the modulus of rupture (f), the specified compressive strength (f), and the modulus of elasticity (E.) for the concrete the beam was made of. Neglect the beam self weight in the calculations. 1/3 3 kN 13 3 kN 13 150 mm 1 = 1.4 m 100 mm

The beam under consideration was subjected to flexure and failed when the maximum tensile stress due to flexure reached the modulus of rupture.Determine the bending moment diagram for the beam The bending moment diagram for the beam subjected to the given load is shown below. It can be determined from either statics or using the beam diagrams and formulas included in Appendix A.It can be observed from the diagram that the maximum bending moment occurs at the central one-third of the beam span; that is, M_(max)~=1.4kNm2. Determine the modulus of rupture (f_(r)) The modulus of rupture is determined by using the flexure formulaf=(M*y_(t))/(I_(g))where f is the flexural stress, M is the bending moment, y_(t) is the distance from the centroid of the section to the extreme tension fibre, and I_(g) is the moment of inertia of the gross cross-section of a concrete beam around the axis of bending.The following tasks need to be performed to find f_(r) :a) Determine the m ... See the full answer