Introduction / Context:
In steel plate girder detailing, webs sometimes employ tongue plates in lieu of horizontal stiffeners. To prevent web instability and to keep compressive/buckling paths realistic in design checks, the effective depth 'd' of such webs is limited by a codified geometric rule. This question tests the specific multiplier applied to the sum of tongue-plate thicknesses when computing the limiting effective depth.
Given Data / Assumptions:
- Member type: plate girder with web composed using tongue plates and no horizontal stiffeners.
- Definition sought: limiting effective web depth 'd'.
- Comparative limits: subtract tongue-plate depth(s) and subtract a multiple of tongue-plate thickness sum from the clear girder depth between flanges; take the lesser.
Concept / Approach:
Tongue plates act as localized restraints in a web that otherwise lacks intermediate horizontal stiffeners. A conservative limit on effective web depth reflects potential local buckling and the discontinuity introduced by the tongues. Handbooks based on traditional steel codes provide an empirical multiplier on the total tongue-plate thickness to capture this effect for safe design without resorting to advanced stability analysis.
Step-by-Step Solution:
State the rule: d = lesser of (i) clear depth between flanges − sum of tongue-plate depths, and (ii) clear depth between flanges − k * Σ(t_tongue).For webs without horizontal stiffeners but with tongue plates, k is taken as 6.Therefore, the correct multiple is 'six times the sum of the thicknesses of the tongue plates'.
Verification / Alternative check:
This multiplier is consistent with conservative detailing provisions that limit slender unsupported web panels and account for local weakening due to cut-ins and welds at the tongue interfaces.
Why Other Options Are Wrong:
Eight times / four times / ten times: not the standard multiplier; adopting them would make the effective depth either too restrictive or unconservatively large.'None of the above': incorrect because an established multiplier exists.
Common Pitfalls:
Confusing tongue-plate depth (a geometric subtraction) with tongue-plate thickness (used in the multiplier).Applying the rule to webs that already have horizontal stiffeners, where different limits apply.
Final Answer:
six times the sum of the thicknesses of the tongue plates
Discussion & Comments