Effective Moment of Inertia of a Reinforced Concrete BeamNOTE: Because reinforced concrete...

Effective Moment of Inertia of a Reinforced Concrete Beam

NOTE: Because reinforced concrete beams crack due to tensile stresses created by moment and shear, initial elastic deflections are based on an empirical equation for moment of inertia established from experimental studies of full-size beams (provided in the ACI Code). This equation produces an effective moment of inertia I_e that varies from about 0.35 to 0.5 of the moment of inertia I_G based on the gross area of the cross section. The additional deflection due to creep and shrinkage that occurs over time, which can exceed the initial deflection, is not considered.

Computer study—Influence of supports on frame behavior. (a) Using the RISA-2D computer program, compute the initial elastic deflection at midspan of the girder in Figure P8.44, given that the support at D is a roller. For the computer analysis, replace the tapered members by 3-ft-long segments of constant depth whose properties are based on each segment’s midspan dimensions; that is, there will be 9 members and 10 joints. When you set up the problem, specify in GLOBAL that forces are to be computed at three secions. This will produce values of forces at both ends and at the center of each segment. To account for cracking of the reinforced concrete, assume for girder BCD that I_e = 0.35I_G; for column AB assume I_e = 0.7I_G (compression forces in columns reduce cracking). Since deflections of beams and one-story rigid frames are due almost entirely to moment and not significantly affected by the area of the member’s cross-section, substitute the gross area in the Member Properties Table.

(a) Replace the roller at support D in Figure P8.44 by a pin to prevent horizontal displacement of joint D, and repeat the analysis of the frame. The frame is now an indeterminate structure. Compare your results with those in part (a), and briefly discuss differences in behavior with respect to the magnitude of deflections and moments.

Figure P8.44: