COLLEGE OF ENGINEERING
CIVIL ENGINEERING DEPARTMENT
CE71: PRINCIPLE OF STEEL DESIGN
----------------------------------------------------------------------------------------------------------MODULE 6C: ECCENTRICALLY LOADED BOLTS-SHEAR
Design Criteria
𝑅𝑛⁄
𝜙𝑅𝑛 ≥ 𝑟𝑢 (𝐿𝑅𝐹𝐷) ,
Ω ≥ 𝑟𝑠 (𝐴𝑆𝐷)
𝜙 = 0.75
Ω = 2.0
Bolt Shear Capacity/Design strength for shear in bolts
𝜙𝑅𝑛 = 𝜙𝐹𝑛𝑣 𝐴𝑏
Required Total/Resultant Shear force in most critical bolt
2
2
𝑟𝑣 = √(𝑟𝑝𝑥 + 𝑟𝑚𝑥 ) + (𝑟𝑝𝑦 + 𝑟𝑚𝑦 )
The direct shear in each bolt due to the applied load is
𝑃𝑦
𝑃𝑥
𝑟𝑝𝑥 =
𝑟𝑝𝑦 =
𝑛
𝑛
The shear in the bolt that is most remote or farthest from the centroid of the bolt group due to
the applied moment is
𝑇𝑐𝑦
𝑇𝑐𝑥
𝑟𝑚𝑥 =
𝑟𝑚𝑦 =
𝐽
𝐽
Twisting moment/Torque at center of group bolt
𝑇 = 𝑃𝑥 𝑒𝑦 + 𝑃𝑦 𝑒𝑥
𝐽 = Polar moment of inertia of the bolt group (mm⁴/mm²)
𝐽 = 𝐼𝑥 + 𝐼𝑦
For bolts with the same cross-sectional area within a bolt group.
𝐽 = ∑(𝑐𝑥 2 + 𝑐𝑦 2 )𝑖
Where
𝑟𝑝 = Force in each bolt due to applied load with components 𝑟𝑝𝑥 , 𝑟𝑝𝑦
𝑃 = Applied load on the connection, with components 𝑃𝑥 , 𝑃𝑦
𝑛 = Total number of bolts.
𝑟𝑚 = Force in each bolt due to applied moment with components 𝑟𝑚𝑥 , 𝑟𝑚𝑦
𝑐 = Radial distance from the centroid of the bolt group with components 𝑐𝑥 , 𝑐𝑦 in the X-and
Y-axes, respectively,
𝑒 = Load eccentricity (i.e., distance from the load to the centroid of the bolt group with
components 𝑒𝑥 , 𝑒𝑦 ),
Shear stress in most critical bolt
𝑟𝑣
𝑓𝑣 =
𝐴𝑏
EXAMPLE 1 (ELASTIC METHOD)
For the bracket connection shown in Figure
STD4. The bolts are 19-mm.-diameter Group B
A490N. Nominal Shear Strength of fastener in
Bearing-Type Connections, 𝐹𝑛𝑣 = 469𝑀𝑃𝑎
Determine the ultimate load Pu, using the elastic
method.
Direct Shear Components
𝑃𝑢
𝑟𝑝𝑥 = 0 , 𝑟𝑝𝑦 =
8
The shear in the bolts due to the eccentricity
𝑒 = 165𝑚𝑚
Twisting moment about the center of bolt group
𝑀 = 𝑃𝑦 𝑒𝑥 = 𝑃𝑢 𝑒 = 165𝑃𝑢
For the farthest bolt from the centroid
𝑐𝑥 = 37.5𝑚𝑚 ,
𝑐𝑦 = 112.5𝑚𝑚
Nominal Shear Strength in Bearing-Type
Connections,
𝐹𝑛𝑣 = 469𝑀𝑃𝑎 (Group B A490N Bolt)
Polar moment of inertia
𝐽 = ∑(𝑐𝑥 2 + 𝑐𝑦 2 ) = 67,500𝑚𝑚4 /𝑚𝑚2
For the farthest or most remote bolt from the
centroid of the bolt group the x- and ycomponents of the shear in the bolt due to
the applied moment is
𝑟𝑚𝑥 = 0.275𝑃𝑢
𝑟𝑚𝑦 = 0.092𝑃𝑢
The ultimate capacity of the bolt (farthest
from the centroid)
Design Criteria
𝜙𝑅𝑛 ≥ 𝑟𝑢
2
2
𝜙𝐹𝑛𝑣 𝐴𝑏 = √(𝑟𝑝𝑥 + 𝑟𝑚𝑥 ) + (𝑟𝑝𝑦 + 𝑟𝑚𝑦 )
𝑷𝒖 = 𝟐𝟖𝟒, 𝟖𝟔𝟓. 𝟔𝟒𝟖𝑵
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