THE UNIVERSITY OF CALGARY Department of Civil Engineering ENCI 461 – Mechanics of Solids and Structures Fall 2014 Practice Problems – Set 4 – Influence Lines Problem 1: Construct the influence line for the vertical reactions at A and at B of the beam in Figure 1.
Figure 1 Problem 2: Construct the influence line for the shear at section C of the beam in Figure 2.
Figure 2 Problem 3: Using the influence lines for the reactions at A and at B of the beam in Figure 3, construct the influence line for the shear at section C of the same beam.
Figure 3 Problem 4: a) Construct the influence line for the moment at section C of the beam in Figure 3. b) Using the influence lines for the reactions at A and at B of the beam in Figure 3, construct the influence line for the moment at section C of the same beam.
ENCI 461 – Fall 2014 – Practice Problems - Set 4 . . . . .Dr. Mamdouh El-Badry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Page 1-1
Problem 5: Using the influence line for shear at section C of the beam in Figure 2, determine the maximum positive shear that can be developed at section C due to a concentrated moving load of 4000 lb plus a uniform moving load of 2000 lb/ft. Verify your answer using statics. ANS. VC max 3000 5625 8625 lb Problem 6: For the beam in Figure 4, use the Müller-Breslau principle to sketch the influence lines for the vertical reaction at A, the shear at C, and the moment at C.
Figure 4 Problem 7: For the beam in Figure 5, use the Müller-Breslau principle to sketch the influence lines for the vertical reaction at A, the shear at D, and the moment at B.
Figure 5 Problem 8: For the beam in Figure 6, use the Müller-Breslau principle to sketch the influence lines for the vertical reaction at A, the shear at D, and the moment at D.
Figure 6 Problem 9: For the cantilever beam in Figure 7, use the Müller-Breslau principle to sketch the influence lines for the vertical reaction at A, the shear at B, and the moment at B.
Figure 7 Problem 10: For the beam in Figure 8, use the Müller-Breslau principle to sketch the influence lines for the vertical reaction at A, the shear at C, and the moment at C.
Figure 8
ENCI 461 – Fall 2014 – Practice Problems - Set 4 . . . . .Dr. Mamdouh El-Badry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Page 1-2
Problem 11: The beam shown in Figure 9 supports a distributed live load of 1.5 kN/m and a single concentrated load of 8 kN. The dead load is 2 kN/m. Determine: (a) The maximum positive moment at C. (b) The maximum positive shear at C.
ANS.
M C max 13.0 kN·m VC max 6.50 kN
Figure 9 Problem 12: The beam shown in Figure 10 supports a distributed live load of 2 kN/m and a single concentrated load of 6 kN. The dead load is 4 kN/m. Determine: (a) The maximum vertical positive reaction at C. (b) The maximum negative moment at A.
RC max 48 kN M A max 54 kN·m
ANS.
Figure 10 Problem 13: Where should a single 500-lb live load be placed on the beam shown in Figure 11 to cause the largest moment at D? Calculate this moment. Assume the support at A is fixed, B is pinned, and C is a roller.
ANS.
M D max 4.0
kip·ft
Figure 11 Problem 14: Where should the beam ABC shown in Figure 11 be loaded with a 300 lb/ft uniformly distributed live load so it causes (a) the largest moment at point A, and (b) the largest shear at D? Calculate the values of the moment and shear. Assume the support at A is fixed, B is pinned, and C is a roller. ANS. M A max 86.4 kip·ft ; VD max 5.40 kip ENCI 461 – Fall 2014 – Practice Problems - Set 4 . . . . .Dr. Mamdouh El-Badry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Page 1-3
Problem 15: For the simple beam shown in Figure 12, determine the maximum positive shear at section C due to the series of concentrated (wheel) loads which move from right to left over the beam.
VC max 5.375 kip.
ANS. Figure 12 Problem 16:
For the simple beam shown in Figure 13, determine the maximum moment at section C due to the series of concentrated (wheel) loads which move from right to left over the beam.
M C max 57.0 kip·ft.
ANS. Figure 13 Problem 17:
For the beam shown in Figure 14, determine the maximum positive shear at section B due to the wheel loads of the truck moving from right to left.
ANS.
VB max 7.5
kip.
Figure 14 Problem 18: For the beam shown in Figure 15, determine the maximum positive moment at section B due to the wheel loads of the crane shown moving from left to right.
ANS.
M B max 10.8
kN·m.
Figure 15
ENCI 461 – Fall 2014 – Practice Problems - Set 4 . . . . .Dr. Mamdouh El-Badry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Page 1-4
