Tractor trailers beyond a certain length require special permits. As a result, long bridge girders are often brought to the site in multiple parts and spliced together. In order to design the splice for a particular single-span bridge, we need to know the peak shear generated at that splice. To

Question

Tractor trailers beyond a certain length require special permits. As a result, long bridge girders are often brought to the site in multiple parts and spliced together. In order to design the splice for a particular single-span bridge, we need to know the peak shear generated at that splice. To know where to put the traffic load to generate the largest shear, we can construct an influence line.

Accepted Answer

Detailed Analysis:
Identify locations for the unit load:
Reaction locations: A, C
Points of interest: [latex]B^-,B^+[/latex]

Calculate the shear, [latex]V_B[/latex], due to each unit load:
Unit load at A:
FBD:

Apply equilibrium:

[latex]+\circlearrowright \Sigma M_C = 0 = A_y(30 \mathrm{~m}) - 1(30 \mathrm{~m})[/latex]

[latex]A_y = 1 (+↑)[/latex]

Cut at B:

Apply equilibrium:

[latex]+\uparrow \Sigma F_y = 0 = 1 - 1 - V_B[/latex]

[latex]V_B = 0 (↓ + ↑)[/latex]

Unit load at [latex]B^-[/latex]:
FBD:

Apply equilibrium:

[latex]+\circlearrowright\Sigma M_C = 0 = A_y(30 \mathrm{~m}) - 1(8 \mathrm{~m})[/latex]

[latex]A_y = 0.267 (+↑)[/latex]

Cut at B:

Apply equilibrium:

[latex]+\uparrow \Sigma F_y = 0 = 0.267 - 1 - V_B[/latex]

[latex]V_B = -0.733 (↓ + ↑)[/latex]

Unit load at [latex]B^+[/latex]:
FBD:

Apply equilibrium:

[latex]+\circlearrowright\Sigma M_C = 0 = A_y(30 \mathrm{~m}) - 1(8 \mathrm{~m})[/latex]

[latex]A_y = 0.267 (+↑)[/latex]

Cut at B:

Apply equilibrium:

[latex]+\uparrow \Sigma F_y = 0 = 0.267 - V_B[/latex]

[latex]V_B = +0.267 (↓ + ↑)[/latex]

Unit load at C:
FBD:

Apply equilibrium:

[latex]+\circlearrowright\Sigma M_C = 0 = A_y(30 \mathrm{~m})[/latex]

[latex]A_y = 0 (+↑)[/latex]

Cut at B:

Apply equilibrium:

[latex]+\uparrow \Sigma F_y = 0 = 0 - V_B[/latex]

[latex]V_B = 0 (↓ + ↑)[/latex]

Table of points:

Location of Unit Load	[latex]V_B[/latex]
A	0.000
[latex]B^-[/latex]	—0.733
[latex]B^+[/latex]	0.267
C	0.000

Create the influence line:

Question 6.2: Tractor trailers beyond a certain length require special per...

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