CE 330 Introduction to Structural Engineering
Fall 2023
Homework #2
(Assigned: 8/28/2023, Due: 9/6/2023)
Problem 1 (10 points) Five precast concrete bridge girders are spaced L1 = 7.5 ft apart and support a
reinforced concrete deck that is t = 8 in thick (as shown below). The concrete deck has an overhang distance
(beyond the centerline of the outside girder) of L2 = 2 ft, and the length of the bridge (i.e.- the span of the
girders) is L3 = 60 ft. Both the girders and the deck are composed of normal-weight reinforced concrete
(unit weight = 150 lb/ft3). Assuming each girder is supported by a pin at one end and a roller at the other
end:
A) Sketch a free body diagram (FBD) of one of the interior girders and determine the magnitude of the
distributed dead load (wD) supported by the girder in units of lb/ft, along with the reaction forces at the
ends of the girder.
B) Sketch a free body diagram (FBD) of one of the exterior girders and determine the magnitude of the
distributed dead load (wD) supported by the girder in units of lb/ft, along with the reaction forces at the
ends of the girder.
L3
t
L1
L1
L1
L1
L2
Cross-section of each I-shaped concrete girder:
(Dimensions are in units of inches)
L2
b1
h1 = 15 in
h2 = 36 in
b1 = 12 in
b2 = 18 in
h1
b2
h2
Problem 2 (10 points) The floor system shown below consists of a 4 in thick reinforced concrete floor slab
resting on three steel floor beams (Beams AB, CD, and EF), which in turn are supported by two steel girders
(Girders ACE and BDF). Steel columns support the ends of each girder at Points A, B, E and F. [The steel
framing system for this problem is similar to the frame shown at the top left on page 70 of the textbook.]
The cross-sectional area of each steel beam is 19.2 in2 and the cross-sectional area of each steel girder is
32.7 in2. There is also a 6 in thick brick wall that is 9 ft tall and 25 ft long, that bears directly on top of Beam
CD. (Note that the figure below is a “plan view” of the floor system, and the brick wall along line CD is 9 ft
tall “coming out of the page.”) The unit weights of structural materials are 150 lb/ft3 (normal weight
reinforced concrete), 120 lb/ft3 (brick wall), and 490 lb/ft3 (structural hot-rolled steel). Provide an FBD of
Beam CD and an FBD of Girder ACE, showing all the dead loads that act on those members along with the
reaction forces at the ends of each member. [Point loads should be stated in units of lb and distributed
loads should be stated in units of lb/ft.] Also determine the total dead load acting at the top of Column
B.
(A = 19.2 in2)
Problem 3 (10 points) The floor system shown in Problem 2 (above) supports a live load of 100 lb/ft2. Show
the various live loads (only) on FBDs of Beam CD and Girder ACE. [Point loads should be stated in units
of lb and distributed loads should be stated in units of lb/ft.]
Problem 4 (20 points) A corner of the flat roof system in a reinforced concrete building is shown in plan
view below. The tops of reinforced concrete columns are shown as rectangles along lines A, B, and C.
Column A1 is a “corner column” at the exterior of the building. Columns B1, C1, A4, and A7 are “exterior
columns” around the perimeter of the building. Columns B4, C4, B7, and C7 are “interior columns.”
Reinforced concrete girders (12 in wide by 20 in deep) span 30 ft between columns along lines A, B, and C.
Reinforced concrete beams (8 in wide by 14 in deep) span 25 ft between girders (or occasionally between
columns) along lines 1 through 7. The concrete roof slab is 6 in thick and is supported by the concrete
beams and girders. The beams, girders, and columns are normal weight reinforced concrete (unit weight
= 150 lb/ft3). The roof slab is lightweight concrete (weight is 8 lb/ft2 per inch of slab thickness). In addition
to dead loads, the roof system must also support a snow load of 30 psf.
A) Provide an FBD of a beam along line 1 (spanning between columns) and show the dead loads
(including beam self-weight) and snow loads acting on the beam. Label the maximum magnitude of the
distributed load.
B) Provide an FBD of a beam along line 3 (spanning between girders) and show the dead loads (including
beam self-weight) and snow loads acting on the beam. Label the maximum magnitude of the distributed
load.
C) Provide an FBD of a girder along line B (spanning between columns) and show the dead loads
(including girder self-weight) and snow loads acting on the girder. Label the maximum magnitudes of any
distributed loads, and also the magnitudes of any point loads.
D) Determine the total magnitude of the (dead + snow) load acting at the top of the interior column at
the intersection of line B and line 4 (column B4).
E) Determine the total magnitude of the (dead + snow) load acting at the top of the "corner column"
at the intersection of line A and line 1 (column A1).
[NOTE: There are two possible ways to consider point loads at the ends of the girder in Part C) of Problem
5. Either method can be considered correct, depending on how you assume the girders and columns support
the beams. Regardless of which method you use in Part C), your final answers in Parts A), B), D), and E)
should not change.]
25 ft
25 ft
10 ft
10 ft
10 ft
10 ft
10 ft
10 ft