SS 3 (formulas)

 required area for wood beam for shear stress allowable axial compressive stress formula Fa = Kl/r K=effective length l=unbraced length r=radius of gyration Fa=allowable axial comp stress radius of gyration term used in column design equal to I=moment of inertia of a memberA=cross sectional area unit shear stress formula (in a steel beam) fv=actual unit shear stressV=max vertical sheard=overall depth of abeamt=thickness of web horizontal shear stress formula fv=3V/2bd X d/d'fv=horizontal shear stressV=shear forceb=breadthd'=actual depth of beam at the notchd=total depth of beam horizontal shear stress or v=horizontal shearV=vertical shear at section under considerationQ=statistical moment about the neutral axis of the area above the plane under consideration section modulus M=bending moment buckling tendency formula kl/rk=constant determined by fixity at ends*higher k - decreases column load capacityl=unbraced length of columnr=radius of gyration-ratio of a measure of the buckling tendency of a steel column-larger the value of kl/r, greater tendency of a column to buckle, resulting in lower column capacity deflection formula =5wL4/384EIwL=W =5WL3/384EI =KL3/EI w=load per linear footW=total pounds horizontal thrust formula (arches) H=horizontal thrustw=total loadL=lengthh=height magnitude of hydrostatics pressure formula magnitude of hydrostatic pressure=unit weight of liquid X depth water unit weight=62.4 lbs/cubic ft retained earth loads formulas 1)pressure at bottom of wall 2)total pressure 1)pressure at bottom of wall=height X unit weight of equivalent fluid 2)total pressure=pressure at bottom/2 X height of wall snow load reduction formula S=total snow load in lbs/sf*reduce snow load for pitch ovre 20degree and exceeds snow load of 20psf required width of footing (wall footing) required width of footing = total load/bearing soil capacity required area of footing formula (single column footing) required area of footing = total load (include weight of footing)/bearing capacity of soil throat area formula throat area = 0.707 x weld size allowable load per in of weld formula allowable load per in of weld=allowable stress X throat area retaining wall base pressure formula base pressure = equivalent fluid pressure X height retaining wall total earth pressure formula total earth pressure=base pressure X height/2 retaining wall bending moment at base formula bending moment at base = total earth pressure X retain wall = height/3 *distance from centroid of triangle to basebasement = height/2  moment of inertia for rectangle about centroid axis: for rectangle about base: foundation pressure F=foundation pressureP=load on the foundationA=area required for footing required column area required column area= concentric load/axial stress take required expansion due to  or  or P/A=internal stressn=coefficient of expansionE=modulous of elasticity =change in temperature section modulus ratio of the moment of inertia of a beam (I) to the distance from its neutral axis to the most remote fiber (c) *for I-beam:   f=flexural (bending) stressM=bending moment modulus of elasticity (E)  *ratio of unit stress to unit strainP=tensile loadL=original lengthA=area =deflection deflection formula K=constant that depends on the load and loading conditionE=modulus of elasticityI=moment of inertiaL=original length*to reduce deflection, increase I unit tensile stress unit stress = moment uniform load: or w=load in lbs/ftsimple load with concentrated load: *max moment when shear diagram crosses 0 finding required column size using formula 0.30(E)/(I/d)2 *where E is given trial and error:1)test=0.3(E)/(I/d)2 to find allowable stress2)to find required column area=axial load/allowable stress=x3)see if x is adequate to match column areas given formula to calculate deflection change when temperature change  = deflectionn = coefficient of expansion (steel=0.0000065)L = original lengtht = temperature change max bending moment formula Fb=M/S M=FbSM=max momentFb=fiber stress in bendingS=section modulus factor of safety factor of safety=(total vertical load X coefficient of friction)/(earth pressure/2)Xh*ratio of the ultimate strength of a material to its working stress formula for finding the bearing pressure under the base plate *given length of column, axial load, area/size of base plate F=P/A=axial load/area of bearing plateF=bearing pressure max shear formula V=max shear calculating pad footing given dead load and live load, soil bearing value f=P/A or A=P/fA=foundation load/allowable soil bearing pressureA=footing areaP=foundation loadf=allowable soil bearing pressure =(x)(x) x= dimension unit stress formula f=P/Af=unit stressP=load area of a circle r2 triangle formulas      moment capacity formula Mu=moment capacityAs=cross sectional area of tensile reinforcement in sify=specified yield strength of reinforcement d=distance from extreme compression fiber to centroida=depth of rect stress block =strength reduction factor =0.90 for flexure =0.75 spiral col = 0.90 for reinforced conc beam = 0.85 for shear=0.70 tied column unit strain formula  =unit strain =total strainL=original length internal stress formula  n(steel)=0.0000065P/A=internal stressn=coefficient of thermal expansiont=temperature change =change in length flexure formula f=flexural stressM=bending moment =distance from the neutral axis to the fiber under considerationI=moment of inertia finding beam size given: 30ft span load=1800lbs/ft A36 steel P40 (use from reference) 1) max moment = wL2/8=1800x302/8=202,500ft-lbsx12=2,430,000in-lbs2) S=M/Fb=2,430,000/24,000=101.25in3Fb for ASTM A36=24,000psi3) use chart P40 to find S section 20ft span: 25ft span: (244)/(20)4=2.440.50x2.44=1.22" parapet calculations  when parapet is at the roof of the building calculating size of a I-beam 1) calculate or 2) calculate: Z=required plastic section modulusm=max. moment=wL2/8 =1.673) section modulus on chart Authorsabrinarusso ID227748 Card SetSS 3 (formulas) DescriptionStructures Exam Updated2013-07-27T21:13:28Z Show Answers