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CE247 Spring 2014 - Solution Key

Problem 4.1

This problem is straightforward; all three failure modes should be checked for each element

of the bracing member. The only difference would be that Ry, Rt factor should be applied and

expected strength should be calculated, and make sure the tensile yielding of the HSS

member gives the governing capacity to ensure enough ductility under seismic loads. The

following table and graph summarizes key coefficients and failure patterns. Values in red

mean failure to satisfy seismic requirements.

Tensile Yielding Net Section Rupture(NSR) Block Shear Rupture(BSR)

2PL12X3/4 758.2 NSR1.1[a]

NSR1.2[a]

BSR1.1[b]

BSR 1.2[b]

BSR 1.3[b]

PL10X1 421.2 NSR 2.1 433.91(U=1) BSR 2.1 588.9

NSR 2.2 Will not govern BSR 2.2 743.9

NSR2.3 391.5

(welded side U=0.75 Ae=Ag)

BSR 2.3 807

BSR 2.4 734.4

BSR 2.5 630.0

BSR 2.6 890.95

HSS 567.4 402k (U=1-x/L=0.807) 591.62

[a]Failure pattern is the same with NSR2.1 - 2.3, but since the thickness of 2PL12x3/4 will be

bigger than one PL10x1, NSR1.1&1.2 will not govern[b]Failure pattern is the same with BSR1.1 & 1.2, but since the thickness of 2PL12x3/4 will be

bigger than one PL10x1, BSR1.1&1.2 will not govern

BSR2.1

BSR2.2

BSR2.4

BSR2 6

BSR2.5

BSR2.3

BSR1.1

BSR1.2

NSR2.1

NSR2 2

BSR1.3

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As can be seen from the summary, the main failure is due to the PL10x1. The following

improvement methods could be carried out:

- Increase the thickness of PL10X1- Increase the width of PL10X1 or reduce the deducted area due to bolts- Increase the weld length to increase U factorProblem 4.2

The following items should be checked,

The three failure modes for tension member and the pin connected end The geometric requirement for the eye-bar

This may seem to be trivial for checking, but they are also important requirements to ensure

the behavior of the connection

The welded connection between eye-bar and pin connected endSince it is welded, An=Ag, so no need to check net section rupture, and yielding capacity has

already been established in the first item, only BSR needs to be checked for this part.

Tensile

Yielding

Net Section

Rupture(NSR)

Shear

Rupture

Block Shear

Rupture(BSR)

Eyebar 1296 1734.6 1040.7 -

Pin end 3600 902.85 2336.3BSR1

BSR2

3135

3110.4

Problem 4.3

The cable force can be established by 3D projection of the loads that come from the

corresponding tributary area of deck. Both ASD and LRFD method are acceptable. In real

practices, ASD is more commonly used for bridge engineering.

Problem 4.4

For current code requirement, the rebar and steel section are assumed to yield at the same time

and provide the tension capacity together. This is, strictly speaking, cant reflect the real behavior,

but for simplicity and the ductile material property of steel, this method is allowed.

BSR1

BSR2

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C E247 Spring 2014

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C E247 Spring 2014

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C E247 Spring 2014

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