Module 6: Steel Tension Members - Examples & Applications

Module 6: Steel Tension Members - Examples & Applications

Tensile Yielding and Rupture

Basic: Design Tensile Strength Calculation

Determine the LRFD design tensile strength (

\phi P_n

) for an A36 steel plate (

F_y = 250 \text{ MPa}, F_u = 400 \text{ MPa}

) with a gross area

A_g = 2,500 \text{ mm}^2

and an effective net area

A_e = 1,800 \text{ mm}^2

LRFD Factors: $\phi_t = 0.90$ for yielding, $\phi_t = 0.75$ for rupture.

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Intermediate: Calculating Net Area with Staggered Holes

15 \text{ mm}

thick steel plate (

A_g = 4,500 \text{ mm}^2

, total width =

300 \text{ mm}

) is under tension. It is connected using

22 \text{ mm}

bolts in a staggered pattern. The hole diameter is taken as

d_h = 22 + 2 = 24 \text{ mm}

. A critical failure path zig-zags across the plate, passing through 3 holes. The staggered path has two diagonal segments, both with a longitudinal pitch (

s

) of

50 \text{ mm}

and a transverse gage (

g

) of

75 \text{ mm}

Calculate the net area (

A_n

) for this specific failure path.

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Advanced: Tension Member with Both Welded and Bolted Connections

A steel tension member (

F_y = 345 \text{ MPa}, F_u = 450 \text{ MPa}

A_g = 4000 \text{ mm}^2

) is spliced. One end is welded (no holes,

U = 0.85

), and the other end is bolted with 4 large bolts (

A_{holes} = 800 \text{ mm}^2, U = 0.90

). Evaluate the design tensile strength of the entire member.

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Effective Net Area (Shear Lag)

Basic: Calculating Shear Lag Factor for an Angle Section

Determine the Shear Lag Factor (

U

) for an L

150 \times 100 \times 10

angle connected by its long leg to a gusset plate using a single line of four

20 \text{ mm}

bolts spaced at

75 \text{ mm}

on center.

Given Parameters:

Centroid distance from the connected leg ( $\bar{x}$ ): $28 \text{ mm}$
Number of bolts in line ( $n$ ): $4$
Bolt spacing ( $s$ ): $75 \text{ mm}$

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Conceptual: Understanding Shear Lag in W-Shapes

A wide-flange (W-shape) beam is used as a tension member in a large truss. It is connected to the joint by bolting only its two flanges to gusset plates; the web is left unconnected. Explain why the effective net area (

A_e

) will be less than the actual net area (

A_n

) and what physical phenomenon this represents.

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Intermediate: Alternative U Factor for W-Shapes

A W-shape tension member is connected by its flanges only, with 3 bolts per line in the direction of loading. Determine the applicable shear lag factor (

U

) using the AISC alternative case for W-shapes.

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Block Shear Strength

Advanced: Evaluating Block Shear in a Gusset Plate

10 \text{ mm}

thick steel gusset plate (A36 steel:

F_y = 250 \text{ MPa}, F_u = 400 \text{ MPa}

) is connected to a tension member using a single line of three

20 \text{ mm}

diameter bolts.

The connection geometry dictates:

Gross shear area ( $A_{gv}$ ): $2,000 \text{ mm}^2$
Net shear area ( $A_{nv}$ ): $1,400 \text{ mm}^2$
Net tension area ( $A_{nt}$ ): $500 \text{ mm}^2$
Uniform tension stress ( $U_{bs}$ ): $1.0$

Calculate the LRFD design block shear strength (

\phi R_n

) of the gusset plate. Assume

\phi = 0.75

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Intermediate: Block Shear with Welds

An L

100 \times 100 \times 10

angle (

F_y = 250 \text{ MPa}, F_u = 400 \text{ MPa}

) is welded to a gusset plate along its heel and toe. The weld length is

150 \text{ mm}

. Calculate the block shear capacity of the angle.

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Conceptual: Mitigating Block Shear Failure

A design for a heavily loaded tension bracing connection fails the block shear check by

10\%

. The engineer cannot change the thickness of the gusset plate or the size of the member due to architectural constraints. Propose two connection detailing modifications to increase the block shear capacity.

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