A solved problem 10-2 For Beam Adequancy For Shear.
The video used for illustration.
In the solved problem 10-2, a given simple beam under the uniformly distributed load of W21x 55. It is required to check the given section W21x 55 adequacy for shear under the given Dead and Live loads. Two designs are estimated are the LRFD and ASD designs are used. In this post, we will use the manual calculation to get the LRFD and ASD values for nominal shear capacities.
You can click on any picture to enlarge then press the small arrow at the right to review all the other images as a slide show.
A solved problem 10-2, check shear adequacy.
This is a solved problem 10-2, from Prof. McCormack’s book, there is a beam, with W section W21x55, Fy =50ksi.
It is required to check the adequacy of this beam to shear.
The beam span is 20′ and is subjected to dead loads Wd=2kips/ft, including self-weight and a uniform live load LL of 4 kips/ft.
From table 1-1, we get all the relevant data for W21x55. A section of W21x55 is drawn, as shown in the small sketch on the left side. We can find the value of h and tw. h value is 18.76”while the tw=0.375″.
The controlling factor for h/tw as given by the AISC is given by the equation is h/tw=2.24*sqrt(E/Fy), consider E=29000 ksi, Fy=50 ksi, this equation can be re-written as 381.46*1/sqrt(50)=53.90.
We will check the given section value of h/tw; it will be estimated as (18.76/0.375)=50.03, the actual h/tw is less than the controlling factor which is =53.90. Hence the section is adequate for shear.
The next step is to get the nominal shear for the section where Vn=0.60*Fy*(Aw*cv), cv=1, fy=50.0 ksi, A web=d*tw=20.80*0.375=7.80 inch2. The value of Vn=0.60*50*7.80=234.0 kips.
Vult =1.20*Vd+1.60*Vl, Since Wd is 2 k/ ft, the span is 20 ft, then V ULT d=1.20*2*10=24 kips.
While Vul-ll=1.60*(4*10)=64.0 kips.Thus V ult=24.0+64.0=88.0 kips.
For the LRFD calculations for section adequacy for shear stress, we have fv =1, then φv *Vn=1*234.0 =234.0 kips, while Vul=88.0 kips , the section is safe.
For the ASD calculations for section adequacy for shear stress, we have Ωv =1.5, then (1/Ω)*Vn=(1/1.50)*234.0 = 156.0kips, while Vt=(2*10+4*10)=60.00 kips, then the section is safe.
We will explain the AISC code provision for shear.
AISC specification provision for the design of Members for shear.
Chapter G is the designated chapter for the design of members for shear.
Clause G-1 is for the general provisions. G-2 is for members of stiffened and unstiffened webs.
Cv value determination for shear of steel beams.
This is the pdf file used for the illustration of this post.