CIVL 4197
Strucutural Analysis Review
Structures FE Review
Spring 2018
First, let’s review what’s in the FE Reference Handbook
1/30
CIVL 4197
Strucutural Analysis Review
2/30
CIVL 4197
Strucutural Analysis Review
3/30
CIVL 4197
Strucutural Analysis Review
4/30
CIVL 4197
Strucutural Analysis Review
p. 85
5/30
CIVL 4197
Strucutural Analysis Review
Exam Problems
Problem 1: The arch shown below is:
A. B. C. D.
unstable stable and statically determinate stable and statically indeterminate redundant
6/30
CIVL 4197
Strucutural Analysis Review
Problem 1: The arch shown below is: As described in the Structural Analysis section of the NCEES Handbook, the stability and determinacy of an arch depends on whether:
Problem 1: The arch shown below is: As described in the Structural Analysis section of the NCEES Handbook, the stability and determinacy of an arch depends on whether: m=1
r=4
j=2
c=1
3m + r = 3(1) + 4 = 7 3j + c = 3(2) + 1 = 7 3m + r = 3j + c stable and statically determinate
7/30
CIVL 4197
Strucutural Analysis Review
Problem 1: The arch shown below is:
A. B. C. D.
unstable stable and statically determinate stable and statically indeterminate redundant
Problem 2: The frame shown below is:
A. B. C. D.
unstable statically determinate statically indeterminate to the first degree statically indeterminate to the second degree
8/30
CIVL 4197
Strucutural Analysis Review
Problem 2: The frame shown below is: As described in the Structural Analysis section of the NCEES Handbook, the stability and determinacy of an arch depends on whether:
m = 6 and r = 3
3m + r = 21
j = 6 and c = 5
3j + c = 23
21 < 23 unstable
Problem 2: The frame shown below is:
A. B. C. D.
unstable statically determinate statically indeterminate to the first degree statically indeterminate to the second degree
9/30
CIVL 4197
Strucutural Analysis Review
Problem 3: The arch shown below is subjected to both uniformly distributed horizontal and vertical loads. The vertical reaction (kN) at support A is:
A. B. C. D.
25 40 55 20
Problem 3: The arch shown below is subjected to both uniformly distributed horizontal and vertical loads. The vertical reaction (kN) at support A is:
MB 0 MB 0 RAy 40 m 60 kN 10 m 80kN 20 m
RAy 25 kN
10/30
CIVL 4197
Strucutural Analysis Review
Problem 3: The arch shown below is subjected to both uniformly distributed horizontal and vertical loads. The vertical reaction (kN) at support A is:
A. B. C. D.
25 40 55 20
Problem 4: For the structure shown below, what are the reactions (in kN)?
A. B. C. D.
A = 4 kN down, B = 10 kN to left, C = 11.5 kN to right A = 3 kN down, B = 10 kN to right, C = 10.0 kN to right A = 4 kN up, B = 10 kN to left, C = 7.0 kN to right A = 4 kN up, B = 8.5 kN to left, C = 1.5 kN to left
11/30
CIVL 4197
Strucutural Analysis Review
12/30
Problem 4: For the structure shown below, what are the reactions (in kN)? Draw the FBD: A
20 kNm
6m
6m
B 4m 4m
C
3 kN
4 kN
F
y
0 A 4 kN
A 4 kN
Mc 0 4 kN 12 m 3 kN 4 m B 8 m 20 kNm
Fx 0 C B 3 kN
B 10 kN
C 7 kN
Problem 4: For the structure shown below, what are the reactions (in kN)?
A. B. C. D.
A = 4 kN down, B = 10 kN to left, C = 11.5 kN to right A = 3 kN down, B = 10 kN to right, C = 10.0 kN to right A = 4 kN up, B = 10 kN to left, C = 7.0 kN to right A = 4 kN up, B = 8.5 kN to left, C = 1.5 kN to left
CIVL 4197
Strucutural Analysis Review
Problem 5: Which of the following statements regarding planar trusses is correct?
A. B. C. D.
Its members are subjected to combined axial loads, shear forces, and bending moments. Its members must have full moment connections at the joints. For trusses to be stable and statically determinate, all of its supports should have zero translation, but be capable of rotation. Its members are subjected to axial loads only.
Problem 5: Which of the following statements regarding planar trusses is correct? A truss is comprised of slender bars that are connected by frictionless pin joints with no moment connections. In order to have static determinacy, truss supports should not all be restrained against translation. The pinned truss joints are capable of transferring an axial load only. Thus, all elements of a truss are subjected to axial loads only. A. B. C. D.
Its members are subjected to combined axial loads, shear forces, and bending moments. Its members must have full moment connections at the joints. For trusses to be stable and statically determinate, all of its supports should have zero translation, but be capable of rotation. Its members are subjected to axial loads only.
13/30
CIVL 4197
Strucutural Analysis Review
Problem 6: The truss shown below is used as a weighing device. If the gauge at R2 reads 9 kN, what is the weight of mass P?
A. 9 kN B. 12 kN C. 4 kN D. 8 kN
Problem 6: The truss shown below is used as a weighing device. If the gauge at R2 reads 9 kN, what is the weight of mass P? Mc 0 R2 12 m P 12 m
P R2
P 9 kN
A. 9 kN B. 12 kN C. 4 kN D. 8 kN
14/30
CIVL 4197
Strucutural Analysis Review
Problem 7: The force in member CB in truss below is:
A. 4.65 kN tensile B. 4.65 kN compressive C. 47.50 kN tensile D. 8.00 kN compressive
Problem 7: The force in member CB in truss below is: Ax
Bx
By
MB 0 8kN 10 m A x 20 m
Fx 0 A x B x
F
y
0 8 kN By
A x 4 kN B x 4 kN B y 8 kN
15/30
CIVL 4197
Strucutural Analysis Review
Problem 7: The force in member CB in truss below is: Joint B
FBC 4 kN
FBW
8 kN
F
y
0 8 kN FBC FBC 8 kN
A. 4.65 kN tensile B. 4.65 kN compressive C. 47.50 kN tensile D. 8.00 kN compressive
Problem 8: The force in member DE is:
A. B. C. D.
11.2 kN tensile 11.3 kN compressive Zero None of the above
16/30
CIVL 4197
Strucutural Analysis Review
Problem 8: The force in member DE is:
F
y
0
1 FDE 8 kN 8 kN 2
FDE 0
A. B. C. D.
FD FDE
FCE
11.2 kN tensile 11.3 kN compressive Zero None of the above
Problem 9: The forces in members FB and GH in truss are:
A. B. C. D.
FB = 2.5 kN tensile, GH = 11.66 kN tensile FB = zero kN tensile, GH = 11.66 kN tensile FB = zero kN tensile, GH = 11.66 kN compressive FB = zero kN tensile, GH = 10.00 kN tensile
17/30
CIVL 4197
Strucutural Analysis Review
18/30
Problem 9: The forces in members FB and GH in truss are: MC 0
FGH
FCG FDC
Joint B FFB is a zero force member
Problem 9: The forces in members FB and GH in truss are: MC 0 12 kN 10 m FGHy 20 m
12 kN 10 m
6 FGH 20 m 136
FGH
FGHy
FCG
FGH 11.66 kN FDC
Joint B FFB is a zero force member
FGHx
CIVL 4197
Strucutural Analysis Review
19/30
Problem 9: The forces in members FB and GH in truss are:
A. B. C. D.
FB = 2.5 kN tensile, GH = 11.66 kN tensile FB = zero kN tensile, GH = 11.66 kN tensile FB = zero kN tensile, GH = 11.66 kN compressive FB = zero kN tensile, GH = 10.00 kN tensile
Problem 10: A truss carries a vertical load, P, of 90 k. The forces in the truss members AC and BC are 90 k (tension) and 155.7 k (compression), respectively. The truss geometry and member lengths are shown in the figure. Both members a cross-sectional area of 5 in2 and E = 29,000 ksi. The vertical deflection (in.) of the crane in the direction of the applied load is most nearly: P
A. B. C. D.
2.0 in. 1.0 in. 0.8 in. 0.2 in.
CIVL 4197
Strucutural Analysis Review
20/30
Problem 10: A truss carries a vertical load, P, of 90 k. The forces in the truss members AC and BC are 90 k (tension) and 155.7 k (compression), respectively. The truss geometry and member lengths are shown in the figure. Both members a cross-sectional area of 5 in2 and E = 29,000 ksi. The vertical deflection (in.) of the crane in the direction of the applied load is most nearly: Use the unit force method. The vertical displacement of the joint C caused by the loading shown can be determined by applying a unit vertical load at joint C and using the expression:
C
P
members
i 1
fi Fi Li Ai E
Problem 10: A truss carries a vertical load, P, of 90 kips. The forces in the truss members AC and BC are 90 (tension) and 155.7 (compression), respectively. The truss geometry and member lengths are shown in the figure. Both members a cross-sectional area of 5 in2 and E = 29,000 ksi. The vertical deflection (in.) of the crane in the direction of the applied load is most nearly: Member
Fi (k)
fi
Li (in.)
Ai (in2)
fi Fi Li Ai
AC
90
1
480
5
8,640
BC
-155.7
-1.73
277
5
14,922.6
Total
23,562.6
C
P
members
i 1
fi Fi Li 23,562.6 k in. 0.812 in. Ai E 29,000 ksi
CIVL 4197
Strucutural Analysis Review
21/30
Problem 10: A truss carries a vertical load, P, of 90 kips. The forces in the truss members AC and BC are 90 (tension) and 155.7 (compression), respectively. The truss geometry and member lengths are shown in the figure. Both members a cross-sectional area of 5 in2 and E = 29,000 ksi. The vertical deflection (in.) of the crane in the direction of the applied load is most nearly: Member
Fi (k)
fi
Li (in.)
Ai (in2)
AC
90
1
480
5
8,640
BC
-155.7
-1.73
277
5
14,922.6
Total
23,562.6
A. B. C. D.
2.0 in. 1.0 in. 0.8 in. 0.2 in.
C
P
members
i 1
fi Fi Li 23,562.6 k in. 0.812 in. Ai E 29,000 ksi
Problem 11: A steel beam is carrying a uniformly distributed load (UDL) of 2 kips/ft, the moment of the inertia of the beam is 500 in4. Its vertical deflection at point A (in.) is most nearly:
A. B. C. D.
0.048 in. 0.40 in. 7.68 in. 9.6 in.
CIVL 4197
Strucutural Analysis Review
Problem 11: A steel beam is carrying a uniformly distributed load (UDL) of 2 kips/ft, the moment of the inertia of the beam is 500 in4. Its vertical deflection at point A (in.) is most nearly:
The slopes and deflections of a simply-supported beam under a UDL are given in the Simply Supported Beam Slopes and Deflections table in the NCEES Handbook. B C
wL3 24EI
wL3 24EI
Problem 11: A steel beam is carrying a uniformly distributed load (UDL) of 2 kips/ft, the moment of the inertia of the beam is 500 in4. Its vertical deflection at point A (in.) is most nearly:
There is no load applied over segment AB. Therefore, segment AB remains a straight line with point A deflecting up distance A as:
Deflection at A A B LAB
22/30
CIVL 4197
Strucutural Analysis Review
Problem 11: A steel beam is carrying a uniformly distributed load (UDL) of 2 kips/ft, the moment of the inertia of the beam is 500 in4. Its vertical deflection at point A (in.) is most nearly:
Converting units to inches:
0.167 k in. 240 in. 0.0066 radians wL3 24EI 24 29,000 ksi 500 in 4 3
B
LAB 5 ft . 60 in. A B LAB
60 in. 0.0066 radians 0.40 in.
Problem 11: A steel beam is carrying a uniformly distributed load (UDL) of 2 kips/ft, the moment of the inertia of the beam is 500 in4. Its vertical deflection at point A (in.) is most nearly:
A. B. C. D.
0.048 in. 0.40 in. 7.68 in. 9.6 in.
23/30
CIVL 4197
Strucutural Analysis Review
Problem 12: A unit load moves horizontally from point C to point G over frame ABCDEFG, which of the following is the influence line diagram for the vertical reaction at support A?
A. B. C. D.
Problem 12: A unit load moves horizontally from point C to point G over frame ABCDEFG, which of the following is the influence line diagram for the vertical reaction at support A?
To determine the influence line for Ay, take the moment about point B. MB 0 Ay 20 ft . 1k 30ft . x Ay 1.5
x 20
24/30
CIVL 4197
Strucutural Analysis Review
Problem 12: A unit load moves horizontally from point C to point G over frame ABCDEFG, which of the following is the influence line diagram for the vertical reaction at support A?
A. B. C. D.
Problem 13: For a 100-kip rolling load over a 30-ft simplysupported beam, the maximum end support reaction (kips) is most nearly:
A. 33.3 kips B. 50.0 kips C. 66.6 kips D. 100.0 kips
25/30
CIVL 4197
Strucutural Analysis Review
Problem 13: For a 100-kip rolling load over a 30-ft simplysupported beam, the maximum end support reaction (kips) is most nearly:
The maximum reaction occurs when the rolling load passes over the support A or B.
For x 0
RA 100 k and RB 0 k
For x 30 ft . RA 0 k and RB 100 k
Problem 13: For a 100-kip rolling load over a 30-ft simplysupported beam, the maximum end support reaction (kips) is most nearly:
A. 33.3 kips B. 50.0 kips C. 66.6 kips D. 100.0 kips
26/30
CIVL 4197
Strucutural Analysis Review
Problem 14: Which of the vertical-load influence lines shown below is correct for Member U2U3 of the truss shown below?
Problem 14: Which of the vertical-load influence lines shown below is correct for Member U2U3 of the truss shown below? The upper chord is always in compression
27/30
CIVL 4197
Strucutural Analysis Review
Problem 15: The plan view of a three-story reinforced building is shown below. All columns are 2-ft squares and are centered on the grid lines. The concrete floors and roof are one-way slabs supported on the beams. The floor system weighs 120 psf, including the dead load of the columns. The service dead load, DL, (kips) on an interior column at its base is most nearly:
A. B. C. D.
200 kips 400 kips 600 kips 750 kips
Problem 15: The plan view of a three-story reinforced building is shown below. All columns are 2-ft squares and are centered on the grid lines. The concrete floors and roof are one-way slabs supported on the beams. The floor system weighs 120 psf, including the dead load of the columns. The service dead load, DL, (kips) on an interior column at its base is most nearly: Determine the tributary area of the column at each floor level. The tributary area of a column is the area adjoining the column, which sheds its load to the column.
28/30
CIVL 4197
Strucutural Analysis Review
Problem 15: The plan view of a three-story reinforced building is shown below. All columns are 2-ft squares and are centered on the grid lines. The concrete floors and roof are one-way slabs supported on the beams. The floor system weighs 120 psf, including the dead load of the columns. The service dead load, DL, (kips) on an interior column at its base is most nearly:
Problem 15: The plan view of a three-story reinforced building is shown below. All columns are 2-ft squares and are centered on the grid lines. The concrete floors and roof are one-way slabs supported on the beams. The floor system weighs 120 psf, including the dead load of the columns. The service dead load, DL, (kips) on an interior column at its base is most nearly:
A. B. C. D.
200 kips 400 kips 600 kips 750 kips
29/30
CIVL 4197
Strucutural Analysis Review
Structures FE Review
Spring 2018 Questions?
30/30