22S-Step-by-step guide to solved problem 10-2 for a Beam.

Last Updated on September 12, 2026 by Maged kamel

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

This post has two parts. The first part discusses solved problem 10-2, while the second part discusses nominal Shear for steel beams based on CM#14 and the 2010 specification.

Solved problem 10-2: check Shear adequacy.

This is problem 10-2 from Prof. McCormack’s book. A Beam has a W21x55 section and Fy = 50 k. Check the adequacy of this Beam to Shear.

First, we will start with the LRFD design and estimate the ultimate load and the Ultimate Shear. From the data in the next slide, the ultimate uniform load is 7 kips/Ft, and the ultimate Shear value is 70 kips.

Table 1-1 shows all the relevant data for W21x55. A section of W21x55 is drawn, as shown in the small sketch on the left side. We can determine d, hw, and tw.

The enclosed web height h, or the distance between flanges less the fillets, equals d-2*kdes hw, which is 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 h/tw=2.24*sqrt(E/Fy). Consider E=29000 ksi and Fy=50 ksi. The value equals 53.90.

The next slide shows the Nominal Shear value for the steel Beam. The Shear coefficient is Cv in CM#14 and Cv1 in CM#15.

The ratio of h to tw equals 50.03 and is less than 53.90.

The next step is to get the nominal Shear for the section where Vn=Cv*0.60*Fy*(Aw*d), cv=1, FCv = 1.0 ksi, A web=d*tweb = d*tw = 20.80*0.375 = 7.80 in^2; value of nominal Shear Vn=0.60*50*7.80=234.0 kips.

For LRFD section adequacy calculations for Shear stress, we have Cv = 1; then φv * Vn = 1* 234.0 = 234.0 kips, while Vul = 88.0 kips; the section is safe.

The next slide presents estimates of the steel Beam’s total uniform load and maximum Shear.

For the ASD calculations of section adequacy for Shear stress, we have Ωv = 1.5; then (1/ω) Vn = (1/1.50) × 234.0 = 156.0 kips, while Vt = (210 + 410) = 60.00 kips; the section is safe.

We will explain the AISC code provision for Shear.

AISC specification provision for the design of Members for shear-CM#14.

Chapter G is the designated chapter for designing members for Shear.

Clause G-1 is for the general provisions. Item G2 deals with stiffened and unstiffened steel sections, including W, M, Hp, and S. The other sections not included in G2 are shown in G3, G4, G5, G6, G7, and G8. Please find the data in the next slide image.

A note is provided for steel shapes with h/tw that do not meet the specification requirement of h/tw <= 2.24*sqrt(Fy), such as W44x230 and W40x149.

Cv value determination for Shear of steel beams.

The factor kv is 5 for webs without transverse stiffeners.

The value of Kc in the case of a stiffened web.

The relation between Vn and h/tw for Fy=36ksi.

The next slide shows the relationship between h/tw and Vn, the nominal Shear value. There are four parts: part I is from h/tw = 0 to h/tw = 2.24*sqrt(E/Fy); this Zone has phi = 1 and lambda = -1.50.

Point 1 for the case of Fy=36 ksi is 63.57 and Cv=1, the Vn=1*(d*tw)*(0.60Fy).

The second part is between 2.24*sqrt(E/Fy) and 1.10*sqrt(k*E/Fy). Vn is constant. The third part is between 1.10*sqrt(k*E/Fy) and 1.37*sqrt(Kv/*E/Fy); the cv value is to be estimated, and the nominal Shear value drops linearly.

The last part is from 1.37*sqrt(Kv/*E/Fy) to h/tw=200; the CV value is to be estimated, and the nominal Shear value has a curved drop.

The relation between Vn and h/tw for Fy=50ksi.

Point 1 for the case of Fy=50 ksi is 53.95 and Cv=1, the Vn=1*(d*tw)*(0.60Fy). Point 2 value equals 59.24. Point 3 value equals 73.77.

The relation between Vn and h/tw for Fy=65ksi.

Point 1 for the case of Fy=65 ksi is 47.30 and Cv=1, the Vn=1*(d*tw)*(0.60Fy). Point 2 value equals 52. Point 3 value equals 64.

You can view or download the PDF containing the data for this post from the following Link.

This is the next post: the solved problem-10-2, how to use Table 3-2 for Shear values? 

Here is the Link to Chapter 8, “Bending Members.” A Beginner’s Guide to the Steel Construction Manual, 14^th ed. Section 8.3.1 Shear Behavior.

Here is the Link to Chapter 8, “Bending Members.” A Beginner’s Guide to the Steel Construction Manual, 15^th ed. Section 8.3.1 Shear Behavior.

Here is the Link to Chapter 8, “Bending Members.” A Beginner’s Guide to the Steel Construction Manual, 16^th ed. Section 8.3.1 Shear Behavior.