Question 4.CS.2: A common detail in structural steel building frames is the s...
A common detail in structural steel building frames is the simple shear connection. Circled in CS Photo 4.1 is an example of such a connection, showing a beam attached to a column using a pair of framing angles welded to either side of the beam web and bolted to the column flange. CS Fig. 4.1 further illustrates the details of the connection. Because the flanges of an I-shaped beam primarily resist bending moment and the web primarily resists shear, and because only the web is connected in a simple shear connection, very little bending moment is transmitted through the joint. For this reason, the bending moment at the end of the beam is assumed to be zero, and the joint is analytically modeled as a pin connection. The American Institute of Steel Construction (AISC) publishes the Steel Construction Manual,* which contains numerous aids for the design of steel buildings, as well as the Specification for Structural Steel Buildings (AISC 360-10) that governs their design. In accordance with AISC 360-10, one way that the bolts of a simple shear connection can be designed is as being slip-critical, where the friction of the clamped interface is relied upon to support the end-shear of the beam. If the connection considered in CS Photo 4.1 was designed as slip-critical using ¾-in. AISC Group A bolts, the design aids in Part 10 of the AISC Manual indicate its capacity to be 75.9 kips, provided that standard bolt holes are used and that the surface of the steel at the interface is unpainted clean mill scale. Assuming that friction of the connection governs its design, let’s perform an analysis to confirm this rated capacity. (Note that there could be other factors that govern the overall capacity of the connection, such as the strength of the framing angles.)
STRATEGY: The friction capacity of the connection can be determined using a suitable static coefficient of friction along with the normal force acting on the interface, where this normal force is the clamping force developed by the tensioned bolts. Using the provisions of AISC 360-10, accepted values for the coefficient of friction and the minimum tension for properly installed bolts can be obtained.
*Ref: Steel Construction Manual, American Institute of Steel Construction, 14e, 2011.
MODELING: Treat one of the framing angles as a free body, cutting through the bolts and weld (CS Fig. 4.2). Because there are two framing angles that support the end of the beam, one half of the beam end-shear is shown. The tension in each bolt can be obtained from AISC 360-10, where the minimum tension in a properly installed ¾−in. Group A bolt is listed as 28 kips. Because the average bolt tension in a proper installation can be expected to be somewhat higher than this minimum, the specification allows an increase of 13%. For unpainted clean mill scale steel surfaces, AISC 360-10 specifies a static friction coefficient μ = 0.30 that can be used to determine the friction force.
ANALYSIS: Normal Force. Each bolt force is the minimum prescribed tension, increased by 13%, or
T_{\text{bolt}} = 1.13(28 kips)= 31.64 kips
Applying equilibrium (CS Fig. 4.2):
+\rightarrow \Sigma F_x=0: \quad 4 T_{\text {bolt }}-N=4(31.64 \text{ kips})-N=0 \quad \pmb{N}=126.56 \text { kips } \leftarrowMaximum Friction Force. The magnitude of the maximum friction force that can be developed is
F_m=\mu N=(0.30)(126.56 \text{ kips})=37.968 \text{ kips}Capacity of Connection. The capacity of the connection reflects the beam end-shear V_{\text {beam }} that can be supported. Applying equilibrium (CS Fig. 4.2):
\begin{aligned}+\uparrow \Sigma F_y=0: \quad-0.5 V_{\text {beam }}+F_m=-0.5 V_{\text {beam }}+37.968 \text{ kips}=0 & \\V_{\text {beam }}=75.9 \text{ kips} \quad \text { (checks) }\end{aligned}REFLECT and THINK: A slip-critical bolted connection is intended not to slip under the maximum anticipated design loads. Should an overload situation occur that does cause the connecting elements to slip, the connection won’t actually fail unless the bolts shear off, or unless the parts that the bolts bear against fail in bearing. Often this involves loads much greater than those necessary to cause slip, thereby adding to the overall margin of safety.
