In reality, though, reinforced concrete beams are rarely simply supported.Instead, concrete floor and roof structures are most often cast monolithically, and designed as indeterminate,continuous structures. Continuous beams and T-beamsįor simply-supported, determinate beams, no special guidelines are required for the calculationof shear and moment. Check actual design moment: since the actual design moment = 3098 in-kips ≤ φ M n = 3726 in-kips (the available moment capacity of the beam), the section is OK for bending. The steel ratio, ρ = A s /( bd) = 3.16/(12 × 25) = 0.0105.įrom Appendix Table A-5.9 or from Equation 5.13, R = 0.552 ksi (this is obtained directly from Equation 5.13 when using Appendix Table A-5.9, interpolate between values for ρ, or, conservatively, use the closest but smaller value of ρ to find R).įrom Equation 5.12, φ M n = φ bd 2 R = 0.9(12)(252)(0.552) = 3726 in-kipsĤ. The curved distribution of stresses within the compressive zone (above the neutral axis for"positive" bending) corresponds to the nonlinear stress-strain curves characteristic of plain concrete,with a value of 0.85 f c' taken for the strength of concrete corresponding to its behavior in anactual structure (Figure 5.19, curve b).įigure 5.26: To find maximum moment for Example 5.4, draw ( a) loading and moment diagram or ( b) free-body diagram cut at midpoint with equation of moment equilibriumįrom A Appendix Table A-5.5, φ = 0.9 for bending.įrom Appendix Table A-5.2, the area of four No. Since tension yielding is the required mode of failure- compressive crushing of the concrete would be sudden and catastrophic, whereas yielding ofthe steel provides warning signs of collapse - concrete beams are deliberately under-reinforced toguarantee that, in the case of failure, the steel reinforcing bars begin to yield before the concrete inthe compressive zone crushes.Īt the point of failure, the stresses in a reinforced concrete cross section are as shown in Figure5.22. Failure of the beam occurs eitherwith crushing of the concrete within the compression region or yielding of the tension steel, followedby compressive crushing of the concrete. The strength, or capacity, of a reinforced concrete beam can be determined by considering theequilibrium of tensile and compressive forces at any cross section. of cover, measured fromthe outside face of the beam to the centerline of the reinforcing steel, is used to protect the steelfrom corrosion, provide fire resistance, and insure adequate bond between the steel and concrete(see Figure 5.17).įigure 5.21: Relationship of bending moment and position of tension steel reinforcement with (a) simply-supportedsingle-span beam and (b) multi-span beam The pattern of steel reinforcement thuscorresponds to the pattern of positive and negative bending moments within the beam: in regionsof positive bending, steel is placed at the bottom of the cross section in regions of negative bending,steel is placed at the top (Figure 5.21). Unlike wood and steel, which can withstand substantial tensionstress, concrete may be safely stressed only in compression. 5 Appendix Chapter 5 - Reinforced concrete: Beams and slabsĬoncrete beams are reinforced with steel rods (reinforcing bars) in order to resist internal tensionforces within the cross section. Introduction to reinforced concrete | Material properties | Sectional properties | Design approaches | Construction systems | Tension elements | Columns | Beams | Connections | Ch.
0 Comments
Leave a Reply. |