
Concept explainers
Find the slope

Answer to Problem 16P
The slope at point B of the given beam using the direct moment-area method is
The deflection at point B of the given beam using the direct moment-area method is
The slope at point C of the given beam using the direct moment-area method is
The deflection at point C of the given beam using the direct moment-area method is
Explanation of Solution
Given information:
The Young’s modulus (E) is 29,000 ksi.
The moment of inertia (I) is
Calculation:
Consider flexural rigidity EI of the beam is constant.
Show the free body diagram of the given beam as in Figure (1).
Refer Figure 1,
Consider upward is positive and downward is negative.
Consider clockwise is negative and counterclowise is positive.
Since support C is a free end there is no reaction.
Determine the bending moment at A;
Determine the bending moment at B;
Determine the moment at D;
Determine the bending moment at C;
Show the
Elastic curve:
The sign of
Show the elastic curve diagram as in Figure (3).
The slope at point B can be calculated by evaluating the change in slope between A and B.
Express the change in slope using the first moment-area theorem as follows:
Here, b is the width of the respective triangle and rectangle and h is the height of the respective triangle and rectangle.
Substitute 10 ft for b,
Determine the slope at B using the relation;
Substitute
Hence, the slope at point B is
The deflection of B with respect to the undeforemd axis of the beam is equal to the tangential deviation of B from the tangent at A.
Express the deflection at B using the second moment-area theorem as follows:
Substitute 10 ft for b,
Determine the deflection at B using the relation;
Substitute
Hence, the deflection at B is
Express the change in slope using the first moment-area theorem as follows:
Here, b is the width and h is the height of the rectangle, triangle, and parabola.
Substitute
Determine the slope at C using the relation;
Substitute
Hence, the slope at point C is
The deflection of C with respect to the undeforemd axis of the beam is equal to the tangential deviation of C from the tangent at A.
Express the deflection at C using the second moment-area theorem as follows:
Determine the deflection at C using the relation;
Substitute
Hence, the deflection at C is
Want to see more full solutions like this?
Chapter 6 Solutions
Structural Analysis, Si Edition (mindtap Course List)
- REINFORCED CONCRETE DESIGNFLEXURAL ANALYSIS OF BEAMS (CRACKED SECTION)Solution must be completeUse ballpen/inkpenAnswer in two decimal placesBox your final answerarrow_forwardWhat is the volume of the earth's mantle in cubic kilometers? (tute problem 4d) Note: enter the number without units. For large (or small) numbers, use E notation, e.g. three million is equivalent to 3*10^6 which is 3E6 in E notation.arrow_forwardH.W: From an in-out survey conducted for a parking area consisting of 40 bays, the initial count was found to be 20 vehicles. Table gives the result of the survey. The number of vehicles coming in and out of the parking lot for a time interval of 5 minutes is as shown in the table below. Find the accumulation, total parking load, average occupancy and efficiency of the parking lot. Table: In-out survey data Time (minutes) In Out 5 3 2 10 6 2 15 3 1 20 6 7 25 6 4 30 8 6arrow_forward
- can you show me step for step? Autocad has me irritated.arrow_forwardmummins) Is there any risk from a contaminant if 150 out of 3800 people exposed to the groundwater contaminant develop cancer and 125 out of 5000 people not exposed to the contamination also develop cancer? Why or why not? Use at least two methods to support your answer.arrow_forwardA spare buoy is a buoyant rod weighted to float and protrude vertically, as shown in thefigure below. Suppose that the buoy is made of maple wood ( specific gravity s = 0.6), has arectangular cross section ( 2.54cm by 2.54cm ), a length of 3.7 m , and is floating in seawater( specific gravity s =1.025 ). What weight of steel should be added to the bottom end of thebuoy so that h=0.45 cm? ( The specific gravity of steel s = 7.85 )arrow_forward
- 8-42. Determine the displacement at point D. Use the principle of virtual work. El is constant. 60 kN 2m- 2 m B 30 kN/m 3 marrow_forwardTwo monitoring wells are spaced 500 m apart along the direction of groundwater flow in a confined aquifer 30.0 m thick. The difference in water level in the wells is 2.5 m. The hydraulic conductivity is 40 m/d. a) Sketch the aquifer and wells and label distances and direction of groundwater flow. b) If the real velocity of the groundwater is 0.6 m/d, what is the porosity? c) If it takes 10 years for a petroleum hydrocarbon plume to appear in the second well, what was the retardation factor?arrow_forward9. 0000) Water in a lake contains 10.5 ppb of vinyl chloride, which has a potency factor of 2.3 (mg/kg-d) 1 a. What is the incremental cancer risk for children (average weight of 15 kg) who may ingest 0.05 L of water per day while playing in the water every summer (for approximately 60 days) for 10 years? b. Is this risk acceptable? Why or why not?arrow_forward
- 8-37. Determine the displacement of point C. Use the method of virtual work. El is constant. -12 ft- 3 k/ft -12 ft- Barrow_forward6. If the initial DO concentration of a diluted (1/50) wastewater sample is 9.0 mg/L and the UO concentration decreases to 2.4 mg/L after 5 days of incubation, a. calculate the 5-day BOD concentration in mg/L: b. If the wastewater degrades at a rate of 0.22/day, what is the ultimate BOD concentration? c. Based on the k value in part (b), what would the BOD concentration be after 10 days? d. What other factor may influence the BOD that is not accounted for in part (c)?arrow_forward2nYour consulting firm is doing an expansion project for a drinking water treatment plant in a growing urban area that has a current population of 55,000 people and treats 20 MGD. If there is 2.8% population growth, continuously compounded, and you want the expansion to be able to serve the urban area for the 35 year design life of the upgraded facility, what should the new design capacity (in MGD) of the treatment plant be?arrow_forward
