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RESEARCH
UNIVERSITI TEKNOLOGI MALAYSIA

UNIVERSITY

SAB 4333
REINFORCED CONCRETE
DESIGN 2

ASSIGNMENT 2
BRACED and
UNBRACED FRAMES

LECTURER: ASSOC. PROF. DR. RAMLI ABDULLAH

1
'.

Ql. Part of the plan of a three storey reinforced concrete building which is to be
constructed without any bracing structures, and the front view of its substitute
frame are shown in Figure Q I. The beams in the substitute frame have a cross
-section of 300 x 600 mm, and are continuous over two spans of 10m each.
The columns with a cross-section of 350 x 450 mm and positioned as shown in
the figure, are 4.5 m high for the first storey and 3.6 m for the successive
storeys. The bottom end of the first lift of the columns may be assumed fixed
to the foundation. The overall thickness of the slab is 150 mm.

The actions on the building are as follows:

Variable action = 4.0 kN/m2
2
Permanent action (excluding self-weight) = 1.2 kN/m
2
Horizontal action from the wind in the E-W direction = 1.5 kN/m

(i) Analyse the sub-frame which consists of Beam 5/A-C, Levelland the
associated upper and lower columns, due to vertical actions with a load
factor of 1.2 for both permanent and variable actions and draw its
bending moment diagram.

(ii) Using' Cantilever Method' obtain the bending moments in all beams
and columns in the substitute frame on gridline 5 due to horizontal
action with a load factor of 1.2, and draw its bending moment diagram.

(iii) Draw the bending moment diagram for the combination of the vertical
and horizontal actions on the sub-frame described in (i). Comment on
the results obtained in view of the design of individual members in the
structure.

2
"

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FIGURE Ql

3
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Q2. Part of the floor plan of a six storey reinforced concrete building and the front
view of its transverse substitute frame are shown in Figure Q2. The lateral
forces on the building in both directions are resisted by shear walls. The
transverse beams, with a cross-section of250 x 600 mm, are continuous over
three spans of 7.0 m, 9.0 m and 7.0 m. The continuous beams in the
longitudinal direction of the building have a cross-section of250 x 600 mm and
a span of 4.0 m. The columns with a cross-section of 300 x 450 mm, and
positioned as shown, are 4.5 m high for the first storey and 3.5 m for the
successive storeys. For the purpose of analysis, the bottom end of the first lift
of the column may be assumed fixed to the foundations. The overall thickness
of the slab is 150 mm. Other relevant dimensions and detailing are also given
in the figure. The building is to be designed for the following vertical actions.

Characteristic variable action 4,0 kN/m2

Characteristic permanent action from finishes, 1.5 kN/m2
services, etc (excluding the self-weight)

Analyse the sub-frame which consists of Beam S/A-D, Level 2, and the
associated upper and lower columns, using One Level Sub-Frame method, and
Set I loading arrangements. Draw the bending moment envelop for the sub-
frame, showing all the important values. ( The maximum span moments should
be determined from shear force diagrams ).

Set I loading arrangements:

(a) Any two adjacent spans loaded with the design variable and permanent
actions, and all other spans loaded with only the design permanent action.
(b) Alternate spans loaded with the design variable and permanent actions,
other spans loaded with only the design permanent action.

4
"

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FIGURE Q2

5
"

Q3. Part of the plan view of a four storey reinforced concrete building which is to
be built without any bracing members, and the front view of its substitute
frame are shown in Figure Q3. All the beams are 250 x 600 mm cross-section.
The beams in the transverse direction are continuous over 8.0 m and 5.0 m,
and the beams in the longitudinal direction are continuous over several spans
of 4.0 m each. The columns which are 350 x 350 mm cross-section, are 4.5 m
high for the first storey and 3.4 m for the successive storeys. The overall depth
of the floor slabs is 175 mm. The building will be designed to carry the
following actions:

2
• Characteristic variable action = 4.0 kN/m
2
• Characteristic permanent action (excluding selfweight) = 1.5 kN/m
2
• Characteristic wind action = 1.2 kN/m

(a) Using One Level Sub-frame Method, analyse the sub-frame consisting of
Beam 2/A-C, Level I with the associated upper and lower columns,
subjected to vertical actions only, taking a factor of 1.2 for both the
permanent and variable actions.

(b) Using the Cantilever Method, analyse the substitute frame shown in
Figure Q3 due to horizontal action only, taking the factor of 1.2.

(c) Sketch the bending moment diagrams for each loading (a) & (b) and the
combined loadings.

(d) For the purpose of designing the members in the sub-frame, what are
other action cases need to be considered? Explain how the bending
moments obtained from here are used in conjunction with the appropriate
values in (c) above.

6
"

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FIGURE Q3

7
.,

Q4. Part of the plan ofa four storey reinforced concrete building and the front view
of its substitute frame are shown in Figure Q4. The lateral forces on the
building in both directions are to be resisted by shear walls. The transverse
beams with a cross-section of 300 x 700 mm, are continuous over two spans of
8.75 m each. The continuous beams in the longitudinal direction of the
building have a cross-section of 250 x 600 mm and a span of 5.0 m. The
columns, with a cross-section 300 x 400 mm, are 4.8 m high for the first lift,
and 3.6 m for the successive lifts, and for the purpose of analysis the bottom
end of the first lift of the column may be assumed fixed to the ground beams /
footings. The overall thickness of the slab is 175 mm. Other relevant
dimensions and detailing are also shown in the figure. The building is to be
designed to carry the vertical actions as follows:

Characteristic variable action 4.0 kN/m2

Characteristic permanent action from finishes 1.5 kN/m2
and services only

(a) Analyse Beam 6/A-C, Levell using the One Level Sub-frame method
AND Continuous Beam plus One Free Joint Sub-frame method, with
loading arrangements suggested in EC2, and draw their respective bending
moment envelopes for the beams only, showing all the important values.
(The maximum span moments should be determined from shear force
diagrams).

(b) Comment on the two sets of the bending moment values obtained in (a).
What effect will these bending moment envelopes have on the amount and
detailing of the reinforcement to be provided in Beam 6/A-C.

(c) Without calculating the amount of reinforcement required in Beam 6/A-C,

show suitable detailing of the main reinforcement at support A for the
analysis in accordance with the two methods used in (a).

B
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All units in mm

8750

FIGURE Q4

9
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Q5. Figure Q5 shows the front view of the first three storeys of a substitute frame
in a 12 storey building which is going to be constructed with shear walls at
suitable locations in the plan to carry the horizontal loads from the wind in
both directions. The beams in the substitute frame are continuous over three
spans of 6.0 m, 8.0 m and 6.0 m, and are of 250 x 600 mm cross-section. The
columns, which are 300 x 400 mm cross-section and positioned as shown
in the figure, are 4.0 m high for the first storey and 3.5 m for the successive
storeys. The lower end of the first lift of the columns may be assumed to be
fixed to the ground beam. The maximum and minimum ultimate actions on all
three spans are 50 kN/m and 20 kN/m respectively.

Determine the bending moments in Beam A-D ( Levell) and the associated
upper and lower columns, using these three methods; (a) One level sub-frame
(b) Two free-joint sub-frame, and, (c) Continuous beams together with one
free-joint sub-frame, and draw their respective bending moment diagrams.

Consider loading arrangement as follows:

(i) All spans loaded with the design variable and permanent actions
(ii) Alternate spans loaded with the design variable and permanent actions,
other spans loaded with only the design permanent action.

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Level 2
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Level I l I
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8000
~_6_00_0 -;b
FIGURE Q5

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Q6. Part of the plan of a four storey reinforced concrete building and the front view
of its substitute frame are shown in Figure Q6. The lateral forces on the
building in both directions are resisted by shear walls. The transverse beams
with a cross-section 300 x 650 mm. are continuous over two spans of 8.5 m
each. The continuous beams in the longitudinal direction of the building have
a cross-section 250 x 500 mm and a span of 5.0 m. The columns, with a cross-
section 300 x 400 mm, are 4.5 m high for the first lift and 3.5 m for the others,
and for the purpose of analysis, the lower end of the first lift may be assumed
fixed to the ground beams/foundations. The overall thickness of the slab is 175
mm. Other relevant dimensions and detailing are also shown in the figure. The
building is to be designed to carry vertical actions as follows:

Characteristic variable action 4.0 kN/m2

Characteristic permanent action from 1.5 kN/m2
tinishes and services only

Analyse the sub-frame which consists of Beam S/A-C, Levell together with
the upper and lower columns, using the One Level Sub-frame method, with
Set 2 loading arrangements. Draw the bending moment envelop for the sub-
frame showing all the important values. ( The maximum span moments should
be determined from shear force diagrams ).

Set 2 loading arrangements:

(a) All spans loaded with the design variable and permanent actions
(b) Alternate spans loaded with the design variable and permanent actions,
other spans loaded with only the design permanent action.

II
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All units in mm
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FIGUREQ6

12