chapter-1(混凝土结构设计原理英文课件).ppt

(a) Calculate the maximum concrete tensile stress using the internal couple method. Solution : Calculate the weight of the beam (weight per unit length): Weight of beam=volume per unit length × unit weight = (a) Calculate the maximum concrete tensile stress using the internal couple method. 1. since the beam is homogeneous, elastic, and symmetrical with respect to both the X-X and Y-Y axes, the neutral axis (N.A) is at midheight. Stress and strains vary linearly from zero at the neutral axis (which is also the centroidal axis) to a maximum at the outer fiber. Since the member is subjected to positive moment, the area above the N.A. is stressed in tension. These stresses result from the bending behavior of the member and are shown in figure 1-5. 2. C represents the resultant compressive force above the N.A. T represents the resultant tensile force below the N.A. C and T each act at the centroid of their respective triangles of stress distribution. Therefore, act together to form the internal couple (or internal resisting moment) of magnirude CZ or TZ. (a) Calculate the maximum concrete tensile stress using the internal couple method 3. the internal resisting moment must equal the bending moment due to extent loads at any section. Therefore, M=CZ=TZ 4650 ft-lb(12 in./ft)=C(8 in.) From which C=6975lb = T 4. C= average stress ×area of beam on which stress acts Solving for yields (b) Flexure formula approach: (c) The modulus of rupture is The calculated tensile stress ( ) of 388 psi is about 6% below the modulus of rupture, the stress at which flexural cracking would be expected. Example1-1 is based on elastic theory and assumes the following: (1) a plane section before bending remains a plane section after bending ( the variation in strain throughout the depth of the member is linear from zero at the neutral axis) (2) the modulus of elasticity is constant ; therefore, stress is proportional to strain and the stress distribution throughou