03/23/2011: Section 2.2 - Calculation for Zr
09/20/2011: Modified Fatigue limit State to include Fatigue I and II Limit States.
This worksheet illustrates the design calculations necessary to satisfy fatigue spacing and strength of stud type shear connectors (6.10.10).
Special Unit Definitions:
End span of a continuous bridge.
Composite in the negative flexural region.
Span length greater than 40 foot.
Deck Thickness:
Sacrificial Wearing Surface:
Concrete Compressive Strength:
Girder Flanges at Maximum Positive Moment:
Deck Effective Width:
Width of the Compression Flange:
Thickness of the Compression Flange:
Width of the Tension Flange:
Thickness of the Tension Flange:
Girder Flanges at Centerline Pier (Negative Moment):
Deck Effective Width:
Width of the Compression Flange:
Thickness of the Compression Flange:
Width of the Tension Flange:
Thickness of the Tension Flange:
Web Depth:
Web Thickness:
Compression Flange Yield Strength:
Tension Flange Yield Strength:
Web Yield Strength:
Steel Modulus of Elasticity:
Total Area of Rebar (Top & Bottom):
Distance Centroid of Rebar to Bottom of Slab:
Haunch (Bottom of Deck To Top of Web):
Moment of Inertia Positive Moment Region (short term):
Distance From N.A. To Extreme Bottom Fiber (short term):
Moment of Inertia Negative Moment Region (composite w/rebar):
Distance From N.A. To Extreme Bottom Fiber (composite w/rebar):
Modular Ratio (short term):
Single Lane Average Daily Truck Traffic:
Stud Diameter:
Number of Studs Per Row:
Stud Ultimate Strength:
Height of Stud:
Maximum Live Load Moment Location from left support:
Span Length:
Factored Shear Range At Tenth Points In The Positive Moment Region (Fatigue I Limit State) (Includes Load Modifier,
Factored Shear Range At Tenth Points In The Negative Moment Region (Fatigue I Limit State) (Includes Load Modifier,
Factored Shear Range At Tenth Points In The Positive Moment Region (Fatigue II Limit State) (Includes Load Modifier,
Factored Shear Range At Tenth Points In The Negative Moment Region (Fatigue II Limit State) (Includes Load Modifier,
For this worksheet the shear range at tenth points is input by the user.
Positive moment region of Span 1 (shear ranges shown at tenth points)
Negative moment region of Span 1 (shear ranges shown at tenth points)
The shear studs shall be spaced along the girder to satisfy the Fatigue Limit State.
(6.10.10.1.2-1 & 6.10.10.1.2-2)
Where:
Vf = Vertical shear force range under the applicable fatigue load combination with the fatigue live load taken as specified in Article 3.6.1.4 (Kip)
Q = First moment of the transformed short-term area of the concrete deck about the neutral axis of the short term composite section (in3)
Zr
ns = Number of shear connectors in a cross-section
In = Moment of inertia of the short-term composite section (in4)
Q = Q(slab concrete) + Q(haunch concrete)
Although the flange plates typically vary in the negative moment region, the calculations will use the properties based on the section over the pier.
For stud type shear connectors:
Where the projected 75-year single lane Average Daily Truck Traffic (ADTT)SL is greater than or equal to 960 trucks per day, the Fatigue I load combination shall be used and the fatigue shear resistance for infinite life shall be taken as:
(6.10.10.2-1)
Otherwise , the Fatigue II load combination shall be used and the fatigue shear resistance for finite life shall be taken as:
(6.10.10.2-2)
in which:
(6.10.10.2-3)
in which:
(6.6.1.2.5-3)
where:
number of stress range cycles (n) midspan
(Table 6.6.1.2.5-2)
number of stress range cycles (n) near pier
Away from pier: (Positive Flexure)
Near pier: (Negative Flexure)
Determine Applicable Fatigue Load Combination:
Applicable equations:
Positive Moment region:
Negative Moment region:
Calculate the shear stud spacing due to the fatigue limit state in the positive moment region and negative moment region.
Section 6.10.10.1.2 states that the maximum spacing must not exceed 24" and not less than 6d.
A minimum number of studs is required over the length of the beam to develop adequate horizontal shear resistance on each side of the point of maximum moment within a span.
The minimum number of shear connectors over a region shall be:
(6.10.10.4.1-2)
where:
(6.5.4.2)
Q
P = Total longitudinal shear force
(6.10.10.4.3-1)
where:
Location from first support to maximum positive live load moment location:
The longitudinal shear force (P
P = P
(6.10.10.4.2-2)
(6.10.10.4.2-3)
Total number of studs required:
Required spacing of studs:
Number of rows:
Spacing of rows:
Location from maximum positive live load moment location to centerline of Pier:
The longitudinal shear force (PT), which must be resisted by the studs (maximum live load moment location to the pier), is the summation of the longitudinal force at the positive and negative maximum moment locations.
PT = P
(6.10.10.4.2-6)
(6.10.10.4.2-7)
(6.10.10.4.2-8)
Total number of studs required:
Required spacing of studs:
Number of rows:
Spacing of rows:
Minimum transverse spacing:
Minimum clear distance from edge of flange to stud edge = 1 in