CM 197 Mechanics of Materials Chap 20: Connections Professor Joe Greene CSU, CHICO CM 197 Copyright Joseph Greene 2003 All Rights Reserved

Copyright Joseph Greene 2003 All Rights Reserved Chap 20 Topics Introduction Riveted Connections Strength of Riveted Connections High-strength bolted connections Eccentrically Loaded Riveted or Bolted Connections Welded Connections Copyright Joseph Greene 2003 All Rights Reserved

Copyright Joseph Greene 2003 All Rights Reserved Introduction Introduction Steel structures used in building frames, bridge trusses, cranes, machine components, etc. are assemblies of beams and columns and other types of members joined together. Connection types Rivets, bolts, and welding Riveted Connections Rivet is a short metal pin with a preformed head and a shank that can be worked into a second head following assembly. Connects Plates, structural steel shapes, sheet metals, thin components. Design Transfer forces from one component to another through connection. Shear forces in rivets (9-4) and bearing force (9-5) between rivets and connected plates. Single shear: one section of rivets is subjected to shear forces. Sect 9-4 and 9-5 Double shear: two sections of rivets are subjected to shear forces. Sect 9-4 and 9-5 Copyright Joseph Greene 2003 All Rights Reserved

Copyright Joseph Greene 2003 All Rights Reserved Riveted Connections Riveted Connections Bearing stress distribution is approximated on the basis of an average bearing stress acting over the projected area of the rivet’s shank onto the cross section of a plate, or area td. Fig 9-7c. Assumptions for riveted sections Holes 1/16th in (1.5mm) larger than the rivet diameter are punched or drilled for the insertion of rivets. Rivets completely fill the hole. Friction forces between the connected plates are ignored. Load applied to a member without any eccentricity with respect to the centroid of the rivets is assumed to be shared equally by all rivets. Shear stress is assumed to be distributed uniformly over a section (or two sections) in double shear of a rivet. Bearing stress is assumed to be distributed uniformly over the projected area, td, where t is the thickness of the plate and d is the diameter of the rivet. Stress concentrations at rivet holes in the plate are ignored. Tensile stress is distributed uniformly across the net section of plate. Copyright Joseph Greene 2003 All Rights Reserved

Copyright Joseph Greene 2003 All Rights Reserved Riveted Connections Riveted Connections Sizes: from ½ in to 1 ½ in at increments of 1/8th in. Common sizes are ¾ in and 7/8 in. Steel rivets are classified as ASTM A502 grades 1 and 2 Fig 20-1. Typical arrangements Strength of riveted connection Failure modes Shear failure of rivets. Fig 20-2 a and b Bearing failure when rivets crush. Fig 20-2c. Tension failure when connected plate is torn apart at critical section from weakened holes. Fig 20-2 d. Copyright Joseph Greene 2003 All Rights Reserved

Strength of Riveted Connections Shear strength Strength of a joint based on the shear of the rivets: Ps = n As allow Where, Ps = strength of the joint based on shear at rivets. n = total number of shear planes of the rivets in the joint. As = cross sectional area of a rivet = d2/4 allow = allowable shear stress of the rivet material. Allowable shear stresses for rivets (AISC manual) for both single and double shear are allow = allowable shear stress = 15ksi (103 MPa) for A502-1 allow = allowable shear stress = 20 ksi (138 MPa) for A502-2 Copyright Joseph Greene 2003 All Rights Reserved

Strength of Riveted Connections Bearing strength Strength of a joint based on the bearing of rivets on plates Pb = n t d allow Where, Pb = strength of the joint based on the bearing of rivets on the plate n = total number of shear planes of the rivets in the joint. t = thickness of the plate. d = diameter of the plate. allow = allowable bearing stress of the plate. Allowable bearing stresses on the projected areas allow = allowable bearing stress = allow = 1.35 y Where, y is the yield strength of connected plate. Copyright Joseph Greene 2003 All Rights Reserved

Strength of Riveted Connections Tensile strength Strength of a joint based on the allowable tensile load ng of the plate through the critical section: Pt = bnet d t, allow Where, Pt = strength of the joint based on allowable tension of the plate. bnet = net width of the plate through a critical section bnet = b-n(d + c) b = width of plate n = total number of rivet holes in critical section. t = thickness of the plate. d = diameter of the rivet. c = constant factor equal to 1/8th in or 3mm to be added to the rivet diameter for the size of the hole t,allow = allowable tensile stress of the plate. Allowable bearing stresses on the projected areas t,allow = allowable bearing stress = t,allow = 0.60 y Where, y is the yield strength of connected plate. Copyright Joseph Greene 2003 All Rights Reserved

Strength of Riveted Connections Joint strength Strength of joint is the smallest of Shear strength Bearing strength Tensile strength Joint efficiency Ratio of the joint strength and the strength of the solid plate (with no holes). Expressed as a percentage Joint efficiency = Strength of the joint/strength of solid plate x 100% Example 20-1: Single shear with six rivets Example 20-2: Double Shear with 6 rivets Example 20-3: Double shear with 4 rivets Copyright Joseph Greene 2003 All Rights Reserved

High-strength bolted connections Leading fastener for connections done in the field. Two types of high strength steel bolts. ASTM A325 and A490 Threaded structural bolts with heavy hex heads with D of ½” to 1½” Inserted in holes with an additional 1/16 in for hole clearance. Types of joints Friction type Bolt is tightened to a specified minimum initial tension equal to 70% of bolt tensile strength. Used for structures that are subjected to impact and vibration. No bearing stress is calculated since bolt is not supposed to slip Bearing type Load is transmitted by bearing of the bolts against joints parts. Bolts are tightened until all plies in a joint are in firm contact. Used in structures subjected to a static load. Allowable Bearing stress on the projected area of the bolts is same for rivets. allow = allowable bearing stress = allow = 1.35 y Where y is the yield strength of the connected part. Copyright Joseph Greene 2003 All Rights Reserved

High-strength bolted connections Allowable shear stresses specified by AISC for A325 and A490 bolts are given in table 20-1 Allowable shear stress for a bearing type connection is higher because a smaller factor of safety against slippage is used. Thus, a smaller factor of safety is used for the allowable shear stress. Example 20-5 Example 20-6 Example 20-7 Copyright Joseph Greene 2003 All Rights Reserved

Eccentrically Loaded Riveted or Bolted Connections In previous sections, the line of action of the applied load passes through the centroid of the connectors. The load is assumed to be shared equally by all the connectors. Load can be applied with eccentricity from the centroid Eccentric load produces direct shear as well as torsion/ Rivets are no longer subjected to equal forces. Fig 20-3 Eccentric load is equivalent to direct force, P, and a torque Pe. Direct shear force P is resisted equally by four connectors each with P/r To resist torque, Pe, the resisting force on each is proportional to its distance to the centroid of the connectors, and acts perpendicular to line. Eqn 20-5 Copyright Joseph Greene 2003 All Rights Reserved

Eccentrically Loaded Riveted or Bolted Connections Sum of moments of resisting forces, F1, F2, F3, and F4 = Pe F1d1+F2d2+F3d3+F4d4 = Pe After combining with Equation 20-5 and rearranging Where, K is the ratio of the couple, Pe, and the sum of the distances, d. If the distance d is broken into x and y components If forces are broken into vertical and horizontal components Example 20-8 Copyright Joseph Greene 2003 All Rights Reserved

Copyright Joseph Greene 2003 All Rights Reserved Welded Connections Welding Process of connecting metallic parts by heating the surfaces to a softened or fluid stated and allowing the melted parts to join together. Arc welding Heating the designated surfaces until they melt and flow together. Heat is applied by an electric arc or gas flame. Electric arc welding is used in almost all steel buildings and steel construction. Electrodes are heated which contain a filler metal that is consumed as welding progresses. Designated E followed by a number that denotes the tensile strength. E70, E90, E110, where strength is in Ksi Type of welds Butt welds: End to end connection Fillet welds: Overlap connection. Most structural connections. Copyright Joseph Greene 2003 All Rights Reserved

Copyright Joseph Greene 2003 All Rights Reserved Welded Connections Leg size Strength of Fillet Welds Fillet welds are designated by leg size (fig 20-6) Leg size Smallest inscribed triangle of weld (usually curved) has a leg of the smallest distance from the root to the opposite edge of weld. Throat is the smallest distance from the root to the opposite side of the triangle. Length of throat for welds with equal legs Size * sin 45 = 0.707 * Size Failure usually occurs in the throat. Allowable shear stress is 0.3 times tensile strength of electrode Allowable shear force, q, per inch q = 0.212 u size Allowable load of fillet weld of length L is P = qL allow = 0.30u Copyright Joseph Greene 2003 All Rights Reserved

Copyright Joseph Greene 2003 All Rights Reserved Welded Connections Strength of Fillet Welds Allowable shear force, q, per inch: q = 0.212 u (size) Allowable load of fillet weld of length L is P = qL Example, Allowable shear force q per unit length of a 5/16-in fillet weld with an E70 electrode is Q = 0.212 (70ksi) (5/16in) = 4.64 kips/in If length of 5/16-in fillet in the joint is 10 in, then, Allowable load in joint would be 4.64 kips/in x 10 in = 46.4 kips Maximum Size of Fillet weld Along edges of material less than ¼ in thick, max size = thickness of material. Along edges of material equal to or greater than ¼ in, the max size should be 1/16in less than the thickness of the material Example 20-9 Example 20-10 Example 20-11 Copyright Joseph Greene 2003 All Rights Reserved