The maximum deflection ratio of a simply supported beam with central load W to a cantilever of equal length loaded with W at the tip equals________________?
Show answer Hide answer
Answer: D. 1/16
Explanation
Comparing simply supported central load deflection to cantilever tip load gives a ratio of 1/16. A simply supported beam deflection formula has a denominator of forty-eight. A cantilever beam tip deflection formula has a denominator of three, producing this ratio. Beam deflection formulas depend heavily on boundary support conditions and loading geometry. Cantilevers are fixed at one end and completely free at the other end. Comparing structural behaviors helps engineers understand relative stiffness across different support types.
Structural comparisons assist in preliminary sizing and educational strength of materials studies. Cantilever structures typically deflect much more than simply supported beams under similar loads. Engineers account for these stiffness differences when designing balconies and overhangs. Option A suggests a ratio of one eighth which incorrectly relates the beam stiffnesses. Option B provides a ratio of one tenth which does not match analytical deflection derivations. Option C incorrectly proposes a ratio of one twelfth instead of one sixteenth.
- Subject
- Engineering
- Category
- Civil Engineering
- Topic
- —
- Difficulty
- medium
Related questions
Q1. What is the ratio comparing the total cross-sectional area of a circular profile to the area of its core_______________?
Show answer Hide answer
Answer: D. 16
The core area ratio relative to the total area of a circular profile is sixteen. Calculating the area of the circular core involves specific geometric kernel limits. Comparing total cross-sectional area to core area for...
Q2. A simply supported circular beam subject to central loading develops equal maximum bending and tensile stresses at a length-to-diameter ratio of___________________?
Show answer Hide answer
Answer: C. 1/2
Equating maximum bending stress to direct tensile stress for circular sections yields a specific ratio. Mathematical simplification of circular cross-section formulas under central loading results in a ratio of one-half....
Q3. A simply supported span L carrying a central concentrated load with flexural rigidity EI experiences a maximum deflection of______________?
Show answer Hide answer
Answer: D. WL3/48EL
The maximum deflection of a simply supported beam with central load W is WL cubed over 48EI. Flexural rigidity EI combines the modulus of elasticity with the moment of inertia. Integrating the moment curvature equation f...
Q4. Cantilever tip deflections caused by concentrated loads applied at 1/3 and 2/3 span positions exhibit a ratio of________________?
Show answer Hide answer
Answer: B. 2/7
Cantilever tip deflections from loads at one third and two thirds span exhibit a ratio of two sevenths. Moment area methods calculate the accumulated slope and deflection along the cantilever span. Cubed position distanc...
Q5. Volumetric strain is responsible for generating strain energy behaving such that________________?
Show answer Hide answer
Answer: D. All the above
Volumetric strain energy depends directly on material volume and the square of applied hydrostatic pressure. Dividing by the bulk modulus reflects how stiffer materials store less strain energy under pressure. Combining...
Q6. Strain energy stored by a spring under maximum non-permanent load distortion is designated as______________?
Show answer Hide answer
Answer: B. Proof resilience
Proof resilience is defined as the maximum strain energy stored in a material without permanent distortion. It represents the capacity of a structure to absorb energy safely within its elastic limit. Once loads exceed pr...