Tiêu đề TOPIC 3b_Analysis & Design of Beams.pdf ✅

Created with PTC Mathcad Express. See www.mathcad.com for more information. TOPIC 3B - DETAILING & SERVICEABILITY EXAMPLE I. Floor Plan II. Given Information: Concrete normal weight: γ≔23.6 ―kN―m 3 Slab thickness: hs≔180 mm Superimposed dead load: dsuper≔0.72 kPa Live load: l live≔4.8 kPa Concrete strength: f'c≔34.5 MPa Steel yield strength: fy≔414 MPa Beam B1 dimensions: hb1≔700 mm bb1≔450 mm Girder dimensions: hg≔760 mm bg≔450 mm Beam B2 dimensions: hb2≔760 mm bb2≔450 mm III. Load Calculations: Concentrated load from B1: Slab self-weight load: dslab1≔γ⋅hs=4.248 kPa (Slab is simply- supported.) Dslab1≔dslab1 ⋅――――――= 170 cm -―45 ―cm―2 2 3.133 ―kN―m Slab superimposed load: Dsslab1≔dsuper ⋅――――――= 170 cm -―45 ―cm―2 2 0.531 ―kN―m Slab live load: Llive1≔l live ⋅――――――= 170 cm -―45 ―cm―2 2 3.54 ―kN―m Db1≔γ⋅hb1 ⋅bb1=7.434 ―kN―m
Created with PTC Mathcad Express. See www.mathcad.com for more information. Beam dead load: Db1≔γ⋅hb1 ⋅bb1=7.434 ―kN―m Beam live load: Lb1≔l live ⋅bb1=2.16 ―kN―m Beam superimposed load: Dsb1≔dsuper ⋅bb1=0.324 ―kN―m B1 load to B2: Pb1D≔⎛⎝Dslab1+Dsslab1+Db1+Dsb1⎞ ⎠ ⋅―――= 1100 cm 2 62.82 kN Pb1L≔⎛⎝Llive1+Lb1⎞ ⎠ ⋅―――= 1100 cm 2 31.35 kN Concentrated load from Girder: Slab self-weight load: Dslab2≔dslab1 ⋅ ((430 cm -45 cm))=16.355 ―kN―m Slab superimposed load: Dsslab2≔dsuper ⋅ ((430 cm -45 cm))=2.772 ―kN―m Slab live load: Llive2≔l live ⋅ ((430 cm -45 cm))=18.48 ―kN―m Girder dead load: Dg2≔γ⋅hg ⋅bg=8.071 ―kN―m Girder live load: Lg2≔l live ⋅bg=2.16 ―kN―m Girder superimposed load: Dsg≔dsuper ⋅bg=0.324 ―kN―m G load to B2: PgD≔⎛⎝Dslab2+Dsslab2+Dg2+Dsg ⎞ ⎠ ⋅――――――= 505 cm -30 cm 2 65.365 kN PgL≔⎛⎝Llive2+Lg2⎞ ⎠ ⋅――――――= 505 cm -30 cm 2 49.02 kN Uniform load from B2 self-weight: Beam B2 dead load: Db2≔γ⋅hb2 ⋅bb2=8.071 ―kN―m Beam B2 live load: Lb2≔l live ⋅bb2=2.16 ―kN―m Beam superimposed load: Dsb2≔dsuper ⋅bb2=0.324 ―kN―m Total uniform load: wb2D≔Db2+Dsb2=8.395 ―kN―m wb2L≔Lb2=2.16 ―kN―m Factored loads: Pu11≔1.4⋅Pb1D =87.949 kN Pu12≔1.2⋅Pb1D +1.6⋅Pb1L=125.545 kN Pub1≔Pu12=125.545 kN Pu21≔1.4⋅PgD =91.511 kN Pu22≔1.2⋅PgD +1.6⋅PgL=156.87 kN
Created with PTC Mathcad Express. See www.mathcad.com for more information. Pug≔Pu22=156.87 kN wu1≔1.4⋅wb2D =11.753 ―kN―m wu2≔1.2⋅wb2D +1.6⋅wb2L=13.53 ―kN―m wu≔wu2=13.53 ―kN―m IV. Diagrams: MOMENT DIAGRAM SHEAR DIAGRAM Tub1≔Pub1 ⋅――= bb2 2 28.248 kN ⋅m Tug≔Pug ⋅――= bb2 2 35.296 kN ⋅m B1 is simply-supported. TORSION DIAGRAM
Created with PTC Mathcad Express. See www.mathcad.com for more information. V. Beam Geometry: B1 Thickness: lb≔1100 cm =11 m hminb11≔―= lb 16 687.5 mm hb1=700 mm B2 Thickness: lb2≔860 cm =8.6 m hminb2≔―= lb2 16 537.5 mm hb2=760 mm B2 as L-Beam adjacent to the opening: 6⋅hs=1080 mm sw≔505 cm =5050 mm ―= sw 2 2525 mm ln≔8.6 m-bg=8150 mm ―= ln 12 679.167 mm bf≔bb2+―= ln 12 1129.167 mm bfmid≔1130 mm B2 as T-Beam near the support: