## A solved problem 10-2 For Beam Adequacy For Shear.

**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. The enclosed depth h , or the distance between flanges less the fillets is equal to d-2kdes will be found as equal to 18.76” while the web thickness 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 nominal shear 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 C_{v} =1, then φ_{v} *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. this part is not included in the video.

### 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.

This is a useful external resource for **Shear Strength Limit State**.

This is the next post, the solved problem-10-2, how to use table 3–2 for shear value?