1. CM 197 Mechanics of Materials Chap 20: Connections
Professor Joe Greene
CSU, CHICO
CM 197
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Chap 20
Topics
Introduction
Riveted Connections
Strength of Riveted Connections
High-strength bolted connections
Eccentrically Loaded Riveted or Bolted Connections
Welded Connections
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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
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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.
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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 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.
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6. 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
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7. 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.
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8. 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.
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9. 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
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10. 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.
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11. 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
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12. 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
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13. 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
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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.
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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 = * 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 = u size
Allowable load of fillet weld of length L is P = qL
allow = 0.30u
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Welded Connections
Strength of Fillet Welds
Allowable shear force, q, per inch: q = 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 = (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
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