## Textbooks & Solution Manuals

Find the Source, Textbook, Solution Manual that you are looking for in 1 click.

## Tip our Team

Our Website is free to use.
To help us grow, you can support our team with a Small Tip.

## Holooly Tables

All the data tables that you may search for.

## Holooly Help Desk

Need Help? We got you covered.

## Holooly Arabia

For Arabic Users, find a teacher/tutor in your City or country in the Middle East.

Products

## Textbooks & Solution Manuals

Find the Source, Textbook, Solution Manual that you are looking for in 1 click.

## Holooly Arabia

For Arabic Users, find a teacher/tutor in your City or country in the Middle East.

## Holooly Help Desk

Need Help? We got you covered.

## Q. 3.8

Our company designs and manufactures pre-engineered steel buildings. The structural system uses tapered steel members to create a rigid frame with a pitched roof. The members become thinner near the top, so the frame behaves like athree-hinge arch.

To design the connection between the vertical and diagonal members, we need to know the moment transferred at that point. One of the load cases we need to check is heavy snow on only one side of the roof.  ## Verified Solution

Analysis:
FBD of AC:

$+\circlearrowright ΣM_A = 0 = 0.5 klf (45 ft) (45 ft/2) + C_x (40 ft) + C_y (45 ft)$

$C_x (40 ft) = -C_y (45 ft) – 506 k • ft$

$C_x = -1.125C_y – 12.65 k$

FBD of CE:

$+\circlearrowright ΣM_E = 0 = -C_x (40 ft) + C_y (45 ft)$

$C_x (40 ft) = C_y (45 ft)$

$C_x = 1.125C_y$

Combine the $C_x$ expression with the result from AC:

$1.125C_y = -1.125C_y – 12.65 k$

$2.25C_y = -12.65 k$

$C_y = -5.62 k$

Substitute $C_y$ into the expression for $C_x$:

$C_x = 1.125 (-5.62 k)$  ;      $C_x = -6.32 k$

FBD of BC:

$+\circlearrowright \sum{M_B} = 0 = M_{BC} + 0.5 klf (45 ft)(45 ft/2) + (-6.32 k)(20 ft) + (-5.62) (45 ft)$

$M_{BC} = -127.0k • ft$

FBD of CD:

$+\circlearrowright \sum{M_D} = 0 = (-6.32 k)(20 ft) – (-5.62)(45 ft) + M_{DC}$

$M_{DC} = -126.5 k • ft$

Summary:        $M_{BC} = -127.0 k • ft$

$M_{DC} = -126.5 k • ft$    