Question

Design reinforced concrete beams supporting 80 feet long concrete flooring system. The width of the concrete floor system is 200 feet. The whole of the structural system consists of reinforced concrete beams, reinforced concrete slabs and reinforced concrete columns.

Answer 1

solution - Reinforced concrete Beam members! - stresses in the concrete above the neutral axis is compressire and nomlineraly distributed in the tension zone below the neutral axis, the concrete is assumed to be cracked and the tensile force present to be taken up by reinforcing steel. strainy distribution stress destribution LL T steel Pesisting comple 9 stress 0.003 strain (e) figure & typical stress-stray cure for concrete. Strength Design for Beams strength design method is similar to LRED. There is a nomppal strength that is reduced by a factor (6) which must exceed the factored design stress. For beaup, the concrete only works in compression over a rectangular istress" block above the Neutral axis from elastic calculation and the steel is exposed and reaches the field stress fy.

for stress analysis in reinforced concrete beams the steel is pansformed to concrete Any concrete in tension is assumed to be cracked and to abore to no strength. the steel can be in tension, and is placed in the bottom of beam that has positive sending moment. The neutral axis is where there is no stress and no spain. The concrete above the nental aris (N.A) isim compression. The concrete below the N.A- is considered ineffective. The steel below the N-A is in tension. Because the N.A. is defined by the moment area, we can solve for a Core) knowing that a is the distance from the top of the concrete section to the centroid of the steel, kb. Trz NA- с NAA bat bxox -NA, (d-x)=0 x can be solved by the equation is rearranged into the generic format with a, btc in the bionomie equation ar2+bx+c=0 by x=-bt5b²yac 2a criteria for Beam Design for flexine Design mus omn where $=0.9(when sectim is tension intolled

so for design 6 mn=&T (d-9/2) = & Asfy (d- 9/2) Rein forcement Ratio & The amount of steel reinforcement is limited. To much reinforcement or over-reinforcing with allow the sted to preld before the concrete crushes and there is sudden failine. A beam with the proper amount do steel to allow it to field to failne is said to be under reinforced. reinforcement ratio p= it 27, 0.005, section is tension controlled. strain in tension can be determined from € + = doc At Ey = fy Es AS 0.25 The resistance factor expressions for transitim for and compression controlled sections are- +=0.75 +(€+-by) 0.15 for spiral member 0.005-Ey) &= 0.65+ (Et-Ey) for other member (0.005-Ey) critered for flat slab and flat plate system Design systems with slabs and supporting beams, joints or columns typically hare multiple bays. The hou antal elements can get as one-way or two-way system, most often the flexure resisting elements are continuous having positive and negative pending moments. These moments and shear talnes can be found using beam form conde specified approximate design factors that slap two-way systemy hare drop panels (for shear), whill that plate do not tables

- criteria for Рич -0 column Design - Puc dc Pn factored load 4 resistance factor Pn Nominal load capacity wond combinations 1.40 (Dis dead Load) 1.20+116L (L is live road) for compression &c = 0.ts and pn=0.8spo for sprical section &c= 0.65 and Pn=0.8 Po for tied columns Po = 0.85 fc (Ag - Ast) + fy Ast mhure Po Maximum grial force Columns which have reinforced-ment ratio Pg = Ast Ag Ig = 1% to 2% most economical spiral ties are harder to construct. column with Bending (Beam column) concrete column rarely see only axial force and must be designed for the combined effects for axial oad and bending moment. The interaction diagram tells us the reduction in arial load a column can cany with a bending moments { Ellic for same column G=4 = & ET/16 G= 4 = Reletive stiffnes E=modaus of elasticity I = moment of martia de = length of colum from centre to cente lb = length of column from centret centre where