Find the maximum positive and negative shears and the maximum positive and negative bending moments at point C.

Answer to Problem 6P
The maximum positive shear at point C is
The maximum negative shear at point C is
The maximum positive moment at point C is
The maximum negative moment at point C is
Explanation of Solution
Given Information:
The concentrated live load (P) is 150 kN.
The uniformly distributed live load
The uniformly distributed dead load
Calculation:
Apply a 1 kN unit moving load at a distance of x from left end A.
Sketch the free body diagram of beam as shown in Figure 1.
Refer Figure 1.
Find the equation of support reaction
Take moment about point D.
Consider moment equilibrium at point D.
Consider clockwise moment as positive and anticlockwise moment as negative.
Sum of moment at point D is zero.
Find the equation of support reaction
Apply vertical equilibrium equation of forces.
Consider upward force as positive
Substitute
Influence line for the shear at point C.
Apply 1 kN load at just left of C.
Find the equation of shear force at C of portion AB
Sketch the free body diagram of the section AC as shown in Figure 2.
Refer Figure 2.
Apply equilibrium equation of forces.
Consider upward force as positive
Substitute
Apply 1 kN load at just right of C.
Find the equation of shear force at C of portion CF
Sketch the free body diagram of the section AC as shown in Figure 3.
Refer Figure 3.
Apply equilibrium equation of forces.
Consider upward force as positive
Substitute
Thus, the equations of the influence line for
Find the value of influence line ordinate of shear force
x | Position | Influence line ordinate of |
0 | A | |
4 | B | |
8 | ||
8 | ||
16 | D | 0 |
19 | E | |
22 | F |
Draw the influence lines for the shear force at point C using Table 1 as shown in Figure 4.
Refer Figure 4.
The maximum positive ILD ordinate at point C is
The maximum negative ILD ordinate at point C is
Find the positive area
Here,
Substitute 4 m for
Find the negative area
Here,
Substitute 4 m for
Find the maximum positive shear at point C using the equation.
Substitute 150 kN for P,
Therefore, the maximum positive shear at point C is
Find the maximum negative shear at point C using the equation.
Substitute 150 kN for P,
Therefore, the maximum negative shear at point C is
Influence line for moment at point C.
Refer Figure 2.
Consider clockwise moment as positive and anticlockwise moment as negative.
Find the equation of moment at C of portion AC
Substitute
Refer Figure 3.
Consider clockwise moment as negative and anticlockwise moment as positive.
Find the equation of moment at C of portion CF
Substitute
Thus, the equations of the influence line for
Find the value of influence line ordinate of moment
x | Position | Influence line ordinate of |
0 | A | |
4 | B | 0 |
8 | ||
16 | D | 0 |
19 | E | |
22 | F |
Draw the influence lines for the moment at point C using Table 2 as shown in Figure 5.
Refer Figure 5.
The maximum positive ILD ordinate of moment at C is
The maximum negative ILD ordinate of moment at C is
Find the positive area
Here,
Substitute 12 m for
Find the negative area
Substitute 4 m for
Find the maximum positive moment at point C using the equation.
Substitute 150 kN for P,
Therefore, the maximum positive moment at point C is
Find the maximum negative moment at point C using the equation.
Substitute 150 kN for P,
Therefore, the maximum negative moment at point C is
Want to see more full solutions like this?
Chapter 9 Solutions
Structural Analysis, 5th Edition
- 6. A lake with no outlet is fed by a river with a constant flow of 1200 ft3/s. Water evaporates from the surface at a constant rate of 13 ft3/s per square mile of surface area. The surface area varies with the depth h (in feet) as A (square miles) = 4.5 + 5.5h. What is the equilibrium depth of the lake? Below what river discharge (volume flow rate) will the lake dry up?arrow_forwardProblem 5 (A, B, C and D are fixed). Find the reactions at A and D 8 k B 15 ft A -20 ft C 10 ft Darrow_forwardProblem 4 (A, B, E, D and F are all pin connected and C is fixed) Find the reactions at A, D and F 8 m B 6m E 12 kN D F 4 marrow_forward
- Problem 1 (A, C and D are pins) Find the reactions and A, C and D. D 6 m B 12 kN/m 8 m A C 6 marrow_forwardUniform Grade of Pipe Station of Point A is 9+50.00. Elevation Point A = 250.75.Station of Point B is 13+75.00. Elevation Point B = 244.10 1) Calculate flowline of pipe elevations at every 50 ft. interval (Half Station). 2) Tabulate station and elevation for each station like shown on example 3) Draw Sketcharrow_forward40m 150N B 40marrow_forward
- Note: Please accurately answer it!. I'll give it a thumbs up or down based on the answer quality and precision. Question: What is the group name of Sample B in problem 3 from the image?. By also using the ASTM flow chart!. This unit is soil mechanics btwarrow_forwardPick the rural location of a project site in Victoria, and its catchment area-not bigger than 25 sqkm, and given the below information, determine the rainfall intensity for ARI = 5, 50, 100 year storm event. Show all the details of the procedure. Each student must propose different length of streams and elevations. Use fig below as a sample only. Pt. E-ht. 95.0 200m 600m PLD-M. 91.0 300m Pt. C-93.0 300m PL.B-ht. 92.0 PL.F-ht. 96.0 500m Pt. A-M. 91.00 To be deemed satisfactory the solution must include: Q.F1.1.Choice of catchment location Q.F1.2. A sketch displaying length of stream and elevation Q.F1.3. Catchment's IFD obtained from the Buro of Metheorology for specified ARI Q.F1.4.Calculation of the time of concentration-this must include a detailed determination of the equivalent slope. Q.F1.5.Use must be made of the Bransby-Williams method for the determination of the equivalent slope. Q.F1.6.The graphical display of the estimation of intensities for ARI 5,50, 100 must be shown.arrow_forwardQUANTITY SURVEYINGarrow_forward
